It starts with a few verses about a young Caribbean man asking his father about marrying a girl. His dad tells him that he was cheating on his mother and the girl is really his sister, so he shouldn’t marry her, but don’t tell Mom because she doesn’t know. This continues for two, three, or a hundred times.
The final, and spoiler verse, is that he goes to his mother and tells her about his frustration that he can’t find a girl to marry and repeats his father’s story. Mom tells him that none of these girls are his sister because his father isn’t really his Dad, but he doesn’t know.
I don’t know the song you’re looking for but blues musician R.L Burnside tells the same tale in the form of a joke/story on his 2001 live album Burnside on Burnside.
Hey, Hey! I once asked this very question! As I’d only heard the song sung by the brother of a uni roomie from the Bahamas, and could remember scarce little of the lyric, I thought my chances rather slim.
However, just like here, the Straight Dope did not disappoint!