I assume you mean he can't travel to the US without a visa. So that presents a problem with Belize, where he doesn't need a visa, but the only way I found that a Jamaican can go there from Jamaica is through the US, which they can't do. Catch 22 there. You can take him to Curacao which is Dutch without a visa. There are some smaller islands but I forgot which ones and can't locate my slip of paper with their names. A travel agent should be able to help you especially one in Jamaica that gave me all the info.

Good Luck!