Dominica

If you try searching for films from Dominica, all you get are hits for the Dominican Republic. Search engines tend to work that way. It's not helpful, particularly as the two countries (although in the same part of the Caribbean) aren't even neighbours and aren't linked. They just happen to be named similarly.

A small country, it doesn't have a major film industry, although I have identified a promising title:

Sargasso: A Caribbean Love Story (1991)