Cruises follow the sun, and in the tropical Caribbean climate, that means you can find a trip pretty much all year around. But some times of year are considered off-season, while others are high-season.
If you cruise during the off-season, you can get great deals; on the other hand, if you cruise at the most popular time of year, expect to pay more.
The "high season" in the Caribbean (i.e. when you can expect good weather, when most people want to take vacations, and when you'll pay more) runs from Christmas to the middle of April and again from June 15th through August 15th. (Weather is actually better in the winter than in the summer, but since children are out of school in the summer, that creates a lot of demand during those months.)
Want to save money on your trip?
For Caribbean cruises, prices are quite low the first two weeks right after the Christmas/New Year holidays, so if you can shift your vacation back a bit, you can save big time.