Joseph Exell and H. D. M. Spence's The Pulpit Commentary compares “bar” in Hebrew to “sire” in English:
Verse 12.—Kiss the Son. It is certainly remarkable that we have here a different word for “Son” from that employed in verse 7, and ordinarily in the Hebrew Bible. Still, there is other evidence that the word here used, bar, existed in the Hebrew no less than in the Aramaic, viz. Proverbs 31:2, where it is repeated thrice. It was probably an archaic and poetic word, like our “sire” for “father,” rarely used, but, when used, intended to mark some special dignity.
And as can be seen from Proverbs 31:2, “bar” is very clearly referring to “son”
What, my son [bar]? (“my son” is בְּרִי ‘ber-ee’ here, and is the possessive form of בַּר ‘bar’)
And what, son [bar] of my womb?
And what, son [bar] of my vows?
with Daniel Whedon's Commentary including the following:
[...] In this verse we meet with the unusual word בַּר, (bar,) son, instead of the usual בֵּן, ben. It occurs three times here, and only once elsewhere, in the Hebrew portion of the Bible, (Psalm 2:12,) though it is usual in the Chaldee parts of the book, and is the ordinary Chaldee word for son. Hence some have been disposed to regard this chapter as of Chaldee origin, or, at least, as belonging to the later Hebrew, in which Chaldaisms are found. To this purpose is adduced the form מְלָכִין, (melakhin,) in verse 3, instead of מְלָכִים, (melakhim,) kings. But this conclusion does not necessarily follow, for poetry often avoids common terms, and employs for its peculiar purposes those which are either new, antiquated, or unusual. Besides, bar, in this sense, is not necessarily Chaldee, but may be legitimately derived from bara, (see Gesenius,) or from barar, as a term of affection or endearment — my beloved — my precious one.
“My precious one” being just another way of denoting “my chosen one—pure and separate from all the rest”; or as John says in his gospel: “...the only begotten of the Father, full of grace and truth” (John 1:14, NKJV).
John Gill also attests to this in his commentary of Psalm 2:
Kiss the Son,... The Son of God, spoken of in Psalm 2:7; the word used is so rendered in Proverbs 31:2; and comes from another which signifies to “choose”, and to “purify”, or “to be pure”; hence some render it “the elect” or “chosen One”, or “the pure One”F11; and both agree with Christ, who is God's elect, chosen to be the Redeemer and Saviour of his people, and who is pure [and] free from sin, original and actual.
F11 (בר) (εκλεκτον), Aquila; “purum”, Cocceius; so Kimchi & Ben Melech.
Daniel Whedon's Commentary mentioned that some think Proverbs 31 is Chaldee in origin due to the spelling of the word “kings” with “-in” instead of “-im” in verse 3:
[...] some have been disposed to regard this chapter as of Chaldee origin, or, at least, as belonging to the later Hebrew, in which Chaldaisms are found. To this purpose is adduced the form מְלָכִין, (melakhin,) in verse 3, instead of מְלָכִים, (melakhim,) kings.
Proverbs 31:3 (NKJV)
Do not give your strength to women,
Nor your ways to that which destroys kings [מְלָכִין].
ים (-im) is the usual Hebrew masculine plural ending. However, while comparatively rare, ין (-in) is also Hebrew as can be seen from the following examples (this is not a complete list):
“Life, living, being alive”
Job 3:20 (NKJV)
Why is light given to him who is in misery,
And life [חיים] to the bitter of soul,
Job 10:12 (NKJV)
You have granted me life [חיים] and favor,
And Your care has preserved my spirit.
Job 24:22 (NKJV)
But God draws the mighty away with His power;
He rises up, but no man is sure of life [חיין].
Job 28:13 (NKJV)
Man does not know its value,
Nor is it found in the land of the living [חיים].
Job 33:30 (NKJV)
To bring back his soul from the Pit,
That he may be enlightened with the light of life [חיים].
“Words, speech, utterances”
Job 4:2 (NKJV)
If one attempts a word with you, will you become weary?
But who can withhold himself from speaking [מלין]?
Job 8:10 (NKJV)
Will they not teach you and tell you,
And utter words [מלים] from their heart?
Job 12:11 (NKJV)
Does not the ear test words [מלין]
And the mouth taste its food?
Job 15:3 (NKJV)
Should he reason with unprofitable talk,
Or by speeches [מלים] with which he can do no good?
Job 15:13 (NKJV)
That you turn your spirit against God,
And let such words [מלין] go out of your mouth?
Job 16:4 (NKJV)
I also could speak as you do,
If your soul were in my soul’s place.
I could heap up words [מלים] against you,
And shake my head at you;
Job 18:2 (NKJV)
How long till you put an end to words [מלין]?
Gain understanding, and afterward we will speak.
Job 19:2 (NKJV)
How long will you torment my soul,
And break me in pieces with words [מלים]?
Job 23:5 (NKJV)
I would know the words [מלים] which He would answer me,
And understand what He would say to me.
Job 26:4 (NKJV)
To whom have you uttered words [מלין]?
And whose spirit came from you?
Job 29:9 (NKJV)
The princes refrained from talking [מלים],
And put their hand on their mouth;
Job 32:11 (NKJV)
Indeed I waited for your words,
I listened to your reasonings, while you searched out what to say [מלין].
Job 32:14 (NKJV)
Now he has not directed his words [מלין] against me;
So I will not answer him with your words.
Job 32:15 (NKJV)
They are dismayed and answer no more;
Words [מלים] escape them.
Job 32:18 (NKJV)
For I am full of words [מלים];
The spirit within me compels me.
Job 33:8 (NKJV)
Surely you have spoken in my hearing,
And I have heard the sound of your words [מלין], saying,
Job 33:32 (NKJV)
If you have anything to say [מלין], answer me;
Speak, for I desire to justify you.
Job 34:3 (NKJV)
For the ear tests words [מלין]
As the palate tastes food.
Job 35:4 (NKJV)
I will answer [מלין] you,
And your companions with you.
Job 35:16 (NKJV)
Therefore Job opens his mouth in vain;
He multiplies words [מלין] without knowledge.
Job 36:2 (NKJV)
Bear with me a little, and I will show you
That there are yet words to speak [מלים] on God’s behalf.
Job 38:2 (NKJV)
Who is this who darkens counsel
By words [מלין] without knowledge?
1 Kings 5:6 (NKJV)
Now therefore, command that they cut down cedars for me from Lebanon; and my servants will be with your servants, and I will pay you wages for your servants according to whatever you say. For you know there is none among us who has skill to cut timber like the Sidonians [צדנים].
1 Kings 11:5 (NKJV)
For Solomon went after Ashtoreth the goddess of the Sidonians [צדנים], and after Milcom the abomination of the Ammonites.
1 Kings 11:33 (NKJV)
because they have forsaken Me, and worshiped Ashtoreth the goddess of the Sidonians [צדנין], Chemosh the god of the Moabites, and Milcom the god of the people of Ammon, and have not walked in My ways to do what is right in My eyes and keep My statutes and My judgments, as did his father David.
1 Kings 16:31 (NKJV)
And it came to pass, as though it had been a trivial thing for him to walk in the sins of Jeroboam the son of Nebat, that he took as wife Jezebel the daughter of Ethbaal, king of the Sidonians [צדנים]; and he went and served Baal and worshiped him.
“Ruins, ruinous heaps”
Psalm 79:1 (NKJV)
O God, the nations have come into Your inheritance;
Your holy temple they have defiled;
They have laid Jerusalem in heaps [עיים].
Jeremiah 26:18 (NKJV)
“Micah of Moresheth prophesied in the days of Hezekiah king of Judah, and spoke to all the people of Judah, saying, ‘Thus says the Lᴏʀᴅ of hosts:
“Zion shall be plowed like a field,
Jerusalem shall become heaps of ruins [עיים],
And the mountain of the temple
Like the bare hills of the forest.”’”
Micah 3:12 (NKJV)
Therefore because of you
Zion shall be plowed like a field,
Jerusalem shall become heaps of ruins [עיין],
And the mountain of the temple
Like the bare hills of the forest.
The lack of the definite article before “bar” is not cause for any concern, since, as Samuel Prideaux Tregelles says on page 96 in his Heads of Hebrew Grammar, “In poetry...the article is often omitted....”
Another example of this can be seen in Psalm 8, where “the moon” and “the stars” are written without the definite article:
Psalm 8:3 (NKJV)
When I consider Your heavens, the work of Your fingers,
The moon and the stars, which You have ordained,
כִּֽי־אֶרְאֶה שָׁמֶיךָ מַעֲשֵׂי אֶצְבְּעֹתֶיךָ יָרֵחַ וְכֹוכָבִים אֲשֶׁר כֹּונָֽנְתָּה
Compare this to the prose of Deuteronomy 4, where “the sun” and “the moon” and “the stars” are written with the definite article (the letter He with patach ( הַ ) plus a dagesh (a small dot) in the next letter):
Deuteronomy 4:19 (NKJV)
And take heed, lest you lift your eyes to heaven, and when you see the sun, the moon, and the stars, all the host of heaven, you feel driven to worship them and serve them, which the Lᴏʀᴅ your God has given to all the peoples under the whole heaven as a heritage.
וּפֶן־תִּשָּׂא עֵינֶיךָ הַשָּׁמַיְמָה וְֽרָאִיתָ אֶת־הַשֶּׁמֶשׁ וְאֶת־הַיָּרֵחַ וְאֶת־הַכֹּֽוכָבִים כֹּל צְבָא הַשָּׁמַיִם וְנִדַּחְתָּ וְהִשְׁתַּחֲוִיתָ לָהֶם וַעֲבַדְתָּם אֲשֶׁר חָלַק יְהוָה אֱלֹהֶיךָ אֹתָם לְכֹל הָֽעַמִּים תַּחַת כָּל־הַשָּׁמָֽיִם
See also chapter 13 of An Introduction to Biblical Hebrew Syntax by Bruce K. Waltke and Michael P. O'Connor, where some of the differences between definiteness in Hebrew and English are discussed. Here too it is pointed out that the definite article is often omitted in poetry, and even include as examples some verses from earlier in Psalm 2:
מַלְכֵי־אֶרֶץ [the] kings of [the] earth
אַפְסֵי־אָרֶץ [the] ends of [the] earth
All of the above surely must have played some role in John Calvin's strong stance of preferring to keep “son” in verse 12, as he calls renderings such as “embrace what is pure” strange and forced interpretations:
[...] The Hebrew word בר Bar, signifies both a son and an elect person; but in whatever way you take it, the meaning will remain the same. Christ was truly chosen of the Father, who has given him all power, that he alone should stand pre-eminent above both men and angels. On which account also he is said to be “sealed” by God, (John 6:27) because a peculiar dignity was conferred upon him, which removes him to a distance from all creatures. Some interpreters expound it, kiss or embrace what is pure, which is a strange and rather forced interpretation. For my part, I willingly retain the name of son, which answers well to a former sentence, where it was said, “Thou art my Son, this day have I begotten thee.”
In his own translation of the Psalms, Jerome ultimately decides to go with “Worship purely” in the text itself, but in his commentary renders it as “Worship the Son”:
I am told that he also carps at me for the translation I have given of a phrase in the Second Psalm. In the Latin it
stands: “Learn discipline,” in the Hebrew it is written Nescu Bar; and I have given it in my commentary, Adore the Son; and then, when I translated the whole Psalter into the Latin language, as if I had forgotten my previous explanation, I put “Worship purely.” No one can deny, of course, that these interpretations are contrary to each other; and we must pardon him for being ignorant of the Hebrew writing when he is so often at a loss even in Latin. Nescu, translated literally, is Kiss. I wished not to give a distasteful rendering, and preferring to follow the sense, gave the word Worship; for those who worship are apt to kiss their hands and to bare their heads, as is to be seen in the case of Job who declares that he has never done either of these things, and says “If I beheld the sun when it shined, or the moon walking in brightness, and my heart rejoiced in secret and I kissed my hand with my mouth, which is a very great iniquity, and a lie to the most high God [Job 31:26-28].” The Hebrews, according to the peculiarity of their language use this word Kiss for adoration; and therefore I translated according to the use of those whose language I was dealing with. The word Bar, however in Hebrew has several meanings. It means Son, as in the words Barjona (son of a dove) Bartholomew (son of Tholomæus), Bartimæus, Barjesus, Barabbas. It also means Wheat, and A sheaf of corn, and Elect and Pure. What sin have I committed, then, when a word is thus uncertain in its meaning, if I have rendered it differently in different places? and if, after taking the sense “Worship the Son” in my Commentary, where there is more freedom of discussion, I said “Worship purely” or “electively” in my version of the Bible itself, so that I should not be thought to translate capriciously or give grounds for cavil on the part of the Jews. This last rendering, moreover, is that of Aquila and Symmachus: and I cannot see that the faith of the church is injured by the reader being shewn in how many different ways a verse is translated by the Jews.
Jerome's Apology in Answer to Rufinus. Book 1.
Though Jerome felt it was ambiguous, it couldn't be clearer to Franz Delitzsch, as he argues in his commentary on the Psalms that the rendering of “kiss the Son”
...has been missed by all the ancient versions except the Syriac, as though its clearness had blinded the translators....
Christopher Wordsworth also sides with “son” for “bar” in his notes on the Psalms:
...it is not unreasonable to suppose that the Psalmist may have designedly chosen a less common form (bar instead of ben, which may also have been avoided on account of the word pen in the Hebrew, which follows next), to distinguish the Son, absolutely, namely, Cʜʀɪsᴛ, Who had been already introduced (in v. 7).... What could be a more natural consequence than to add, “Kiss the Son”?
[...] and to take it [בַר bar] as an adverb, purely, is without any parallel instance in the Hebrew Scriptures. [...]
On the whole it seems best to adhere to the rendering of our Authorized Version, “Kiss the Son,” [...].
Our authorized rendering is that of several Hebrew expositors, Abenezra, Maimonides, Mendelssohn, [...].