I believe it would be impossible to give a dogmatic answer on this. However, there are a number of interesting connections to Paul's letters worth considering.
What to Look For
First we need to establish what to look for. Namely the concept stated in the first part of 2 Pet 3:15:
Καὶ τὴν τοῦ κυρίου ἡμῶν μακροθυμίαν - σωτηρίαν ἡγεῖσθε
And the (of the Lord of us) longsuffering, as salvation you all are to be considering it
The Greek structure has two definite articles side by side (τὴν τοῦ; "the the") because the first is in the accusative case and goes with the later word μακροθυμίαν ("the longsuffering"), while the second begins a nested modifier between the first definite article and that word, showing that "of the Lord of us" modifies "the longsuffering." The whole phrase then is the first of two accusatives used in the sentence.
The second accusative is simply σωτηρίαν ("salvation"). There are two accusatives because sometimes the verb ἡγέομαι (here in the present imperative 2nd-person plural middle-passive form of ἡγεῖσθε) takes a double accusative, the meaning of which is to "consider this [first accusative] as this [second accusative]."1
So the ESV translation is good:
And count the patience of our Lord as salvation
I prefer the NKJV...
and consider that the longsuffering of our Lord is salvation
...only because the word "longsuffering" better reflects the idea of μακροθυμίαν. Literally, that word is a compound word from two other Greek words, the adjective μακρός ("long")2 and the noun θυμός (in this context, "anger" or "wrath")3, so μακροθυμίαν means "long to come to anger," (i.e. longsuffering, patient).
So where in Paul's letters do we see the idea of God's anger being restrained for the purpose of people being saved. This is the concept to seek in the letters.
Second, depending on one's views on the epistles of 1 & 2 Peter, there may be a clue in them as to the audience. If taken at face value for authorship (i.e. the apostle Peter is the writer of both), and if the reference in 2 Peter 3:1 stating "I now write to you this second epistle" (NKJV) be taken as a statement that 2 Peter is essentially to the same group as what 1 Peter was written to, then one may have justification to narrow down which specific letters Peter might refer to. This is because 1 Peter was written to people in "in Pontus, Galatia, Cappadocia, Asia, and Bithynia" (1 Peter 1:1). However, do see the discussion below under "Romans?" for another possibility for "second epistle."
If all that is true, then it would refer to either Galatians (in Galatia), Ephesians (in Asia), Colossians (in Asia), or possibly 1 or 2 Timothy (who was ministering in Ephesus after Paul left; 1 Tim 1:3).
Most Likely Candidates
1 Timothy?
Given those two parameters, there is one definite verse that matches very well, 1 Tim 1:16 (NKJV):
However, for this reason I obtained mercy, that in me first Jesus
Christ might show all longsuffering, as a pattern to those who are
going to believe on Him for everlasting life.
The bolded statement is this in Greek:
ἐν ἐμοὶ πρώτῳ ἐνδείξηται Ἰησοῦς χριστὸς τὴν πᾶσαν μακροθυμίαν
in me first he might show (Jesus Christ) - all longsuffering
This mentions the longsuffering in direct connection with Christ. It is in a salvific context in which Paul is relating his own salvation, which is even a demonstration of God's longsuffering with Paul, 1 Tim 1:12-15 (NKJV; emphasis added):
12 And I thank Christ Jesus our Lord who has enabled me, because He
counted me faithful, putting me into the ministry, 13 although I was
formerly a blasphemer, a persecutor, and an insolent man; but I
obtained mercy because I did it ignorantly in unbelief. 14 And the
grace of our Lord was exceedingly abundant, with faith and love which
are in Christ Jesus. 15 This is a faithful saying and worthy of all
acceptance, that Christ Jesus came into the world to save sinners, of
whom I am chief.
The one problem with this being the letter referred to is that it was not really a letter originally addressed to a group (as is Peter's letters). This is not enough to totally discount it, but the "you" in 2 Pet 3:15 (referring to the letter that Paul wrote) is plural in the Greek, which would seem to point more toward one of the church letters.
Ephesians/Colassians (or even Galatians)?
All the other letters that went to Asia/Galatia area mention "longsuffering" (μακροθυμία) as well, but all in the context of what believers are to be themselves, and not God's longsuffering (Gal 5:22 as a fruit of the Spirit; Eph 4:2; Col 1:11, 3:12; 2 Tim 3:10).
However, though Ephesians does not specifically note the idea of God's longsuffering, in 2:1-3 the idea is latent in the fact that believers were "by nature the children of wrath," even as unbelievers still are. Colossians 3:5-7 makes a similar statement about believers past life deserving wrath.
Galatians is less clear, but the concepts of the past (and even present) sinfulness is clear (1:6; 2:15, 17; 3:1; 5:19-21), and their conversion from that (4:8-9). Also Paul as an example of conversion is noted (1:23-24; this matches somewhat with the 1 Timothy idea above). However, the idea of wrath is not expressly stated in it as in Ephesians and Colossians, rather the focus is on the curse (3:10-14), and God's longsuffering seems to be more pictured through Paul's ministry itself (4:19), and his call to patience in helping others who are faltering (6:2).
So the concept of God's longsuffering against those that deserved wrath but instead came to salvation is present in all three letters, though perhaps slightly more explicit in Ephesians and Colossians.
Other Possibilities
If the audience is not the same as 1 Peter, then Paul's other letters open up as more potential candidates as well.
Romans?
The book of Romans as a whole is a commentary about God's longsuffering when mankind deserves wrath. There are two passages in particular, however, that note the relation of wrath, God's longsuffering, and salvation:
Rom 2:4 (NKJV)
Or do you despise the riches of His goodness, forbearance, and
longsuffering [μακροθυμία], not knowing that the goodness of God leads you to
repentance [i.e. salvation]?
This, like the 1 Timothy passage above, makes for a direct parallel to Peter's statement.
Additionally,
Rom 9:22-24 (NKJV)
22 What if God, wanting to show His wrath and to make His power known,
endured with much longsuffering [μακροθυμία] the vessels of wrath prepared for
destruction, 23 and that He might make known the riches of His glory
on the vessels of mercy [i.e. salvation], which He had prepared beforehand for glory,
24 even us whom He called, not of the Jews only, but also of the
Gentiles?
This actually shows more concretely that the wrath is restrained from all deserving it (which as noted previously—especially in Eph 2—even those that end up saved, vessels of mercy, originally were by nature fit for wrath). So God restrains His wrath, that is, He is longsuffering, so that anyone would be saved.
These passages, along with the whole context of Romans, makes it a good candidate if Peter's audience for 2 Peter is in fact the Romans and not the areas noted in 1 Peter.
That it could be Romans is not without some additional merit. Tradition has Peter being in Rome at the end of his life. 2 Peter 1:13-14 appears to be a reference to Peter's approaching death. If tradition and the interpretation of this bit of evidence from v.14 are correct, then 2 Peter would have been written in Rome. Couple that with the way 2 Peter is addressed, to a rather generic audience of believers (1:1), would be more in line with a group to which he is basically handing the letter over to (rather than a letter traveling across miles to a destination). If so, then the reference to the "second epistle" (3:1) would be a second note handed over to the same group, simply indicating that chapters 1-2 were the first note he gave them prior to his death, and chapter 3 a second note, or that the whole epistle is a second letter to the Romans (the first being lost).
So the internal evidence along with tradition can make a strong argument for Romans, and Romans is also the most likely book as a whole for Peter to reference with respect to God's longsuffering bringing salvation.
Conclusion
Again, dogmatism on this is probably not possible. Peter was not clear what letter was being referred to. Really, any of Paul's letters could be considered as covering the topic of God's longsuffering mercy toward sinners, and the salvation that has come to those who believe because God did not kill them for their sin right away.5
Nevertheless, the most likely candidates are the ones noted above, and Romans only if 2 Peter is not considered a continuation to the same audience as 1 Peter.
NOTES
1 William Arndt, Frederick W. Danker, and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000), s.v. ἡγέομαι, 2 (hereafter this is resource is referred to as BDAG).
2 BDAG, s.v. μακρός, 1.
3 BDAG, s.v. θυμός, 2.
4 BDAG, s.v. μακροθυμία, 2b.
5 Given that all Paul's letters broadly hold the theme (as that is true of all those who come to salvation, that God did not immediately kill them for their sin, but gave them time/space to repent and believe), Peter's reference in v.16 "as he [Paul] does in all his letters when he speaks in them of these matters" probably does refer specifically back to the longsuffering of God as salvation idea noted in v.15. The differentiation is that there was a specific letter written "to you" (the same people Peter was addressing had been addressed by Paul) versus the other letters that would have been to others.
