Any time in Oct/Nov/Dec/Jan is usually ok in the caribbean. If it rains its still hot and it usually dries up very fast so it doesn't spoil the fun! I go to the caribbean nearly every winter and the rain has never been bad...just occasional short shower.
We went earlier this month we looked in my husbands dive book and they say the best time to go to the carribean is between january and March I'm sure some other months would be ok but these are the best months and we had super weathe.
I've always gone in late December and/or January (mainly because i feel the the weeks after Christmas tend to be a bit flat and depressing after Christmas) and the weather has always been great. If it does rain, it is usually only for a very short time and it is far enough away from the end of the huurican season, that if an island has been badly hit by one, the cleaning up opration has been completed. I don't see why feb or mar should not be a good time to go either.
In the last few years the Hurricane season has gone on into October and there have been storms in November so if you want to be more sure of getting the best weather January and February are the months to aim for.....Nei.