The Methodist Records of South Eleuthera have some really helpful records (if one can actually read them.) The birth of a child was noted with the addition of the mother's name (good) and the names of the mother's parents (fantastic). Thus the birth record for Elizabeth Morton reads:
"Elizabeth, daughter of of Benjamin and Ann Morton, who was daughter of Richard and Ann Culmer, born at Tarpum Bay 1 October 1834....baptism information here" .
The wills of the Bahamas are on film and if you can identify the year that Richard Culmer's will was proved - your local LDS Family History Library can send for them. The Bahamas Genealogy Group can help you identify which film to order from Salt Lake City.