There is a group called Calennig that has recorded several of the shanties collected by James Madison Carpenter. See their web page called Trade Winds. They give an email address. Maybe they can help you. There is more information about their albums on this page.

Volume 8, Issue 4 of The Folk Music Journal was all about Carpenter. It contains an article called "Here We Come Home in a Leaky Ship!" by Robert Young Walser, about those shanties. I suspect that's the same Bob Walser who recorded a CD called When Our Ship Comes Home, which contains (guess what!) a song called "Down Trinidad"! There is a 9:47 sample available of that CD, and it seems to contain about 30 seconds of each song. About 4:40 into the sample, you come to "Down Trinidad." I transcribed these lyrics:

O tell me master stevedore how you store your cargo
Way-ay-ay sing sunny door
O tell me master stevedore how you store your cargo
Bound down Trinidad to look for sunny door

Would you free me bully boys and burton in the archway?
Way-ay-ay sing sunny door
Would you free me bully boys and burton in the archway?
Bound down Trinidad to look for sunny door

But I transcribed them phonetically and I don't have a clue what they're talking about! But maybe someone else will be able to interpret or correct what I have written.