Is there is a list of which translations of the Bible are accepted by the Southern Baptist Convention?
The Southern Baptist Convention, while the highest authority within the Southern Baptist church, is not technically an authority amongst Baptists. It functions as a voluntary association with which member churches may choose to associate, but cannot dictate terms to anyone. While it does approve changes to the "Baptist Faith and Message," these are to be taken as guidelines not at odds with the local autonomy of the church.
Within the Baptist Faith and Message (the closest thing Baptists have to a creed), it simply says:
The Holy Bible was written by men divinely inspired and is God's revelation of Himself to man. It is a perfect treasure of divine instruction. It has God for its author, salvation for its end, and truth, without any mixture of error, for its matter. Therefore, all Scripture is totally true and trustworthy. It reveals the principles by which God judges us, and therefore is, and will remain to the end of the world, the true center of Christian union, and the supreme standard by which all human conduct, creeds, and religious opinions should be tried. All Scripture is a testimony to Christ, who is Himself the focus of divine revelation.
The BFM itself is silent on which versions are "approved."
That said, I suspect the question wants to know what translations are preferred. Here, any major translation would suffice, I propose the following list to help you figure out which ones are most likely:
Conservative to Evangelical: English Standard Version (ESV), NIV, HCSB (if you went to Dallas Theological Seminary)
Moderate to Scholarly: NRSV, RSV
Moderate to Gender-inclusively liberal: TNIV
Super-traditional: King James Version. Maybe New King James, if they're feeling special.
Conservative but Scholarly: The Amplified Bible.
When the Preacher wants to make a point: NLT, "The Message"
Perhaps more useful would be the ones Baptists would be very unlikely to use:
New Jerusalem Bible, Duoay-Rheims: perceived as too Catholic
New World Translation: restricted to the Jehovah's Witness
Makes most conservatives barf: The Living Bible, Readers Digest Condensed, Good News Translation.