You'll find the Joseph Spence recording of the song on a Smithsonian Folkways album called Joseph Spence: The Complete Folkways Recordings 1958. I can't make out the lyrics he's singing, but the guitar work is wonderful. Follow the link to the notes, which aren't particularly helpful.

As indicated in this thread the version sung by Belafonte is attributed to Norman Span, whoever he was.

The message from Jeri above say the song was written by Trinidadian calypso singer, King Radio in 1946.

It's hard to trace the roots of many of the songs recorded by Harry Belafonte. I think that Caribbean songwriters didn't really see songwriting as a business, so they didn't worry much about claiming ownership of the songs.

-Joe-