See if you can take it back to your great-grandparents. If you can, chances are that you will find at least one hit on one of those four great-grandparents on the LDS database. And, given the LDS arguments for the New World Jesus and their liking of tracking native geneologies, there is a reasonable chance that one of your maternal great-grandparents will be a hit.

Also, the Old South would sometimes make little additional ethnic notations on birth records. See if you can get a photocopy of the actual record from the state, not just a computer verification. Either your grandmother or one (or more) of your maternal great-grandparents may have an extra notation on the actual original record. The state will probably have a microfiche copy of that.

I hope this gives you some leads.