My husband and I cruised on our honeymoon in December (10yrs ago) and we opted for the southern caribbean...the weather was beautiful, and we were much further down in the caribbean to ensure hot, hot weather.
Ah! December is a great month to cruise the Caribbean. Weather is usually pretty consistent year round. So, if you are looking for ideal conditions - just avoid hurricane season and anytime is just about perfect.
The best months for cruising are late August & September, right after school starts, and January & February. You will find ships less crowded at these times. Hoilday sailings are full of kids. Hope this helps!
I wouldn't agree with David that August & September are among the best months for Caribbean cruising. David is correct that there are fewer kids onboard than during the school holidays (while the ships might still be filled to 100% or more). But August & September is Hurricane season and tends to be very hot and humid. January & February is much better IMHO.