We've done a lot in April and May and have always had good weather. June is OK. Late July & August could be rainy as well as a lot of kids. Last week of November and first week of December is a great "price deal" time and weather is OK.
Hurricane season is what you want to make of it - if you go with "it was worth the money" and "we had a great time" attitude, then you will do OK. If you think you get a great deal and then squawk about the seas and the weather, then you should go in the spring.
The cruise lines do a great job of avoiding weather but there are times when, well, it just gets rough.
The temperatures aren't that much different between summer and winter for most of the Caribbean, especially for those of us coming from the North Country (Maine). Warm is warm and very greatful. :O)
Enjoy whenever and wherever you go.