Steve Ray has a list of more than 35 loaded Questions for "Bible Christians" (quotation marks his)(link to the whole list). I originally planned to respond to just 35 of them, but the series seems to have been of interest, so in this extension, I'm responding to three more numbered questions in his list, plus fourteen "bonus questions" that take the form "Where does the Bible say ... ." I'm trying to provide the answers in the same common format as the original series, for easy reference. This is number 8/17.
Where does the Bible . . .
. . . provide a list of the canonical books of the New Testament?
1) Of course, there's an uninspired list provided in the front of most Bibles.
2) If someone had their Bible (assumed in the question) but their Bible didn't have that list, one could go through and create such a list quite easily.
3) But if the question is simply asking whether one of the books of the Bible includes an inspired list of the books of the New Testament, then of course the answer is that no one book provides such a list.
1) Some of the books of Scripture to the canonicity of other books:
1 Timothy 5:18 For the scripture saith, Thou shalt not muzzle the ox that treadeth out the corn. [Deuteronomy 25:4] And, The labourer is worthy of his reward. [Luke 10:7]
2 Peter 3:15-16
And account that the longsuffering of our Lord is salvation; even as our beloved brother Paul also according to the wisdom given unto him hath written unto you; as also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction.
2) Paul's epistles sometimes more and sometimes less explicitly claim divine inspiration
1 Corinthians 14:37 If any man think himself to be a prophet, or spiritual, let him acknowledge that the things that I write unto you are the commandments of the Lord.
2 Corinthians 13:10 Therefore I write these things being absent, lest being present I should use sharpness, according to the power which the Lord hath given me to edification, and not to destruction.
3) Some books of Scripture refer the reader back to other books of Scripture
2 Peter 3:1 This second epistle, beloved, I now write unto you; in both which I stir up your pure minds by way of remembrance:
Acts 1:1 The former treatise have I made, O Theophilus, of all that Jesus began both to do and teach,