I am lucky that my cousin knew that my great grandfather was from St. Kitts. If he did not tell me I would have been in big trouble because the family was always listed as British West Indies on the census. The Mormons actually have tons of islands birth and death indices/records on microfilm that can be sent to your local family search center. People should also try the Ellis Island search database. I've found one or two relatives there who came over in the early 1900s.

Interesting St. Kitts links
http://www.tc.umn.edu/~terre011/genhome.html

http://www.historicbasseterre.com/

My St. Kitts names: Jacobs/Rennix