What is the polite term for native islanders of the Caribbean?

What is the appropriate term to refer to the people native to the Caribbean islands? I need a general term, appropriate for use in schoolwork, similar to the term "Native American", that can refer to all of the people who lived in the Caribbean islanders prior to Columbus’ arrival.

I have some academic books that use "native" and "Native" (capitalized) though these are older books, and I don’t know if either is still PC. "Islander" also isn’t specific enough, as I need to exclude any Spanish who settled down there. Is "Native Caribbean" an acceptable term?