Louisiana iris might grow for you.

Bearded irises rot if there is too much rain, especially warm rain. If the climate of Barbados is anything like Jamaica's, that is too wet and humid for bearded varieties.

Japanese and Siberian irises like cold winters, so they will not live in your climate either.

Here is a link to a seller of lovely Louisiana irises.

Here is a link that might be useful: Zydeco irises