Is there is a list of which tranlations 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 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:
Perhaps more useful would be the ones Baptists would be very unlikely to use:
What about the NASB?
The SBC does not support the TNIV nor the 2011 revision of the NIV because of the inaccurate translations pertaining to gender. There are resolutions stating such.
They were fine with the 1984 NIV, but it is no longer being printed. They now support the HCSB.