This answer was taken from Examining the Trinity.
Even famed Southern Baptist New Testament Greek scholar Dr. A. T. Robertson admits:
“It is not certain whether ho theos is here the vocative [‘your throne, O God’] ... or ho theos is nominative (subject or predicate) with estin (is) understood: ‘God is thy throne’ or ‘Thy throne is God.’ Either makes good sense.” - p. 339, Vol. 5, Word Pictures in the New Testament, Broadman Press, 1960.
However, there is more evidence, evidence which shows not only that Heb. 1:8 may be honestly translated “God is your throne,” but, indeed, should be so translated!
Notice the context. Heb. 1:8 and 1:9 are being quoted from Ps. 45:6 and 45:7. In Ps. 45:7, speaking to the Israelite king, it says:
“Therefore God, your God, has anointed you with the oil of gladness above your fellows.” - RSV.
Just as this makes it clear that the ancient Israelite king was not God but was anointed by God, HIS God, to a position above his fellows, so does Heb. 1:9, as figuratively applied to Jesus, show that he is not God, but was anointed by his God to a position above his fellows! Context, then, shows that the person addressed in Heb. 1:8 is not God, but one who worships God and was anointed by his God!
The renowned Bible scholar, B. F. Westcott, wrote:
“The LXX [Septuagint] admits of two renderings [at Ps. 45:6, 7]: [ho theos] can be taken as a vocative in both cases (‘thy throne, O God, .... therefore, O God, thy God...’) or it can be taken as the subject (or the predicate) in the first case (‘God is Thy throne,’ or ‘Thy throne is God...’), and in apposition to [ho theos sou] in the second case (‘Therefore God, even Thy God...’) .... It is scarcely possible that [elohim] in the original can be addressed to the King. The presumption therefore is against the belief that [ho theos] is a vocative in the LXX. Thus on the whole it seems best to adopt in the first clause the rendering: ‘God is thy throne’ (or, ‘Thy throne is God’), that is, ‘Thy kingdom is founded upon God, the immovable Rock.’” - The Epistle to the Hebrews, London, 1889, pp. 25, 26.
Further evidence for the proper translation of Heb. 1:8 is found in the conclusions reached by the United Bible Societies’ (UBS) Bible Text Committee. The United Bible Societies (composed of the American Bible Society, The National Bible Society of Scotland, The Netherlands Bible Society, and the Wurttemberg Bible Society) appointed an international and interdenominational committee (but trinitarian, of course) of textual scholars to determine the most accurate text possible of the Greek New Testament.
To do this they examined hundreds of variations in the many thousands of ancient New Testament manuscripts and compared other existing texts by Westcott and Hort, Nestle, Bover, and Vogels.
In 1971 the UBS published A Textual Commentary on the Greek New Testament which explained why the committee had chosen certain readings as being correct and rejected others. In choosing the text they believed to be closest to the original manuscript of the book of Hebrews, the UBS committee looked at the very oldest and best manuscripts still in existence today. Several methods helped them decide what is probably the original wording. One, of course, is how many of the very oldest and best manuscripts agree.
Another method is to determine which of the variations were most likely to have been changed by later copyists. For instance, when a NT writer is referring to an OT quotation, he often has it worded slightly differently from the exact quote in the Septuagint (Paul is especially noted for this).
So, if one NT manuscript has an OT scripture quoted exactly as it appears in the Septuagint, and another has a slightly different wording, the manuscript that differs slightly is more likely to have the proper, original wording. (Later copyists strongly tended to “correct” the original NT manuscripts by making their OT quotes conform exactly to the wording in the Septuagint version.)
Another consideration is that later Church copyists would often change the wording of a scripture if it seemed to contradict a teaching of the Roman Church. Therefore, if the wording of an ancient manuscript seems to contradict a later teaching of the Roman Church, it is more likely to have the original wording than another ancient manuscript which (at the same verse) seems to agree with that Church teaching.
Using these criteria, the UBS Committee unanimously agreed with all the wording of Heb. 1:8 except for one word. They agreed that the original writing of Heb. 1:8 should read literally (in the NT Greek): “toward but the son the throne of you the god into the age of the age and the staff of the straightness staff of the kingdom [‘of him’ or ‘of you’].”
It was the very last word of Heb. 1:8 that caused a “considerable degree of doubt” among those textual scholars. This very last word was either the NT Greek word sou (translated into English as “of you” or “your”) or autou (translated “of him” or “his”).
Why is it so important? Because these trinitarian scholars agreed that if autou (“his”) were used here by the author of Hebrews 1:8, then the verse “must be” translated “God is thy throne” and not “thy throne, O God”!! If, however, sou (“your”) was the original wording, then it could be translated either way. Obviously, then, a trinitarian would strongly prefer the reading of sou.
In discussing this problem the UBS Committee noted that most of the very oldest and best manuscripts (p46 - circa 200 A.D.; 'Aleph' - 4th century; and B - 4th century) all agree that the original wording was “his (autou) kingdom.”
They also noted that later manuscripts which read “your (sou) kingdom” are now in agreement with the corresponding passage in the Greek OT Septuagint! (Remember that the UBS Committee recognizes, as do most Bible scholars, that the NT manuscript that differs slightly from the Septuagint is more likely to be correct than another one which perfectly agrees because copyists strongly tended to deliberately “correct” Septuagint quotes they found in the NT .)
Furthermore, since autou is not repeated near the word in question in this NT manuscript quote of Ps. 45:6, 7, but sou is repeated, before and after, it would have been easy for a copyist to have inadvertently miscopied sou here. Autou, then, is more likely to have been original than sou for more than one reason.
It is also important to realize that all the oldest manuscripts (which were probably written before the full trinity doctrine was officially declared by the Roman Church in 381 A. D. and certainly written well before it was popularly accepted through the efforts of such men as Augustine in the early 5th century) use the word autou which will not properly allow for the trinitarian-preferred interpretation. Whereas many of the later manuscripts now use the word sou which will allow for the trinitarian-preferred interpretation of Heb. 1:8.
Isn’t it significant that the very earliest manuscript to use the trinitarian-preferred sou is Manuscript A from the 5th century which is shortly after the trinity doctrine was fully and officially declared at the Council of Constantinople in 381 A. D. and during the highly successful efforts of Augustine and others to defend and popularize this newly established “truth” of the Roman Church? (Remember the correlation between new church doctrines and changes in later manuscripts.) .
So even though there is overwhelming evidence that “his” (autou) was in the original manuscript of Hebrews 1:8 (even the trinitarian scholars who developed the Westcott and Hort text and the Nestle text (NA21) use autou at Heb. 1:8), the UBS Committee finally agreed to choose “your” (sou) and label that choice as “having considerable degree of doubt,” anyway!
Why did they bend their own rules of evidence? Because (1) they said there were so many later manuscripts that used sou, and (2) they admitted that they didn’t like what that verse actually said if autou had really been used in the original!
Oh, they did soften the arbitrariness of their choice slightly by labeling it as “having considerable degree of doubt,” but if any honest impartial scholar will examine their own comments on the evidence, he must agree that the UBS Committee’s choice is purely an emotional one and the evidence rules otherwise (as other trinitarian texts noted above admit).
Sou not only has “considerable degree of doubt,” it is nearly impossible. The UBS Committee’s own comments on the evidence make autou virtually certain as the original word, and, therefore, in the committee’s own word’s, Hebrews 1:8 “must be” translated “God is thy throne” and not “thy throne, O God.” - (study pp. 662-663 in A Textual Commentary on the Greek New Testament, United Bible Societies, 1971.)
Some trinitarians have objected that “it does not make sense [or even, ‘it’s ridiculous’] to call God a ‘throne.’” However, to any serious Bible student, it is entirely reasonable and appropriate. Calling God “the throne of Jesus” is an excellent figurative way to show that God approves and upholds Christ’s kingly reign (as in Westcott’s comment previously quoted).
New Testament texts produced by trinitarians in which Autou (“His”) was chosen as part of the original text ("... the scepter of his [autou] kingdom":
Westcott and Hort
It has been admitted by respected scholars (UBS text writers) that if autou ("his") were in the original writing of Heb. 1:8, the proper rendering earlier in the same verse must be “God is your throne”! – p. 663, A Textual Commentary on the Greek New Testament, United Bible Societies, 1971.
Even the highly respected NASB renders this as "... the scepter of his kingdom." The Jerusalem Bible; New Jerusalem Bible; The New English Bible; Revised English Bible; AT (Smith and Goodspeed); Rotherham; Byington; C.B. Williams; etc. also render it using "his."