It depends on what you want for the best time- best time to get the best deal or the best time to go period. It also depends on what you are looking for as far as your cruise. If you are someone who doesn't want to go when a ship may have a lot of children or if you are hoping to go in a less crowded time. It really depends on what you are looking for.
There is hurricane season which can lower prices but also there are 3 day weekends during hurricane season where the prices are higher due to the demand. Hurricane season is June 1st through November 30th with the majority of hurricanes in August and September.
The winter season is popular (and more expensive) because people from colder climates want to get out of the cold and spend some time in the Caribbean where it is warmer. Also, people that think the Caribbean is too hot during the summer will travel there during other times of the year to be a bit cooler.
Consult a good travel agent (and when I mean good.. I mean someone who will take the time to listen to what your needs are). Websites like Orbitz etc.. won't give you that personalized attention and counseling a good travel agent can offer!
You might also want to take a look at the cruise line promos and discounts. The cruise lines provide a lot of them now as they want to increase the popularity of cruising. Just because there is a promotional discount doesn't necessarily mean you will end up on a less crowded cruise ship. The promotions are there so the cruise line can fill the ship. They never want to sail with any empty cabins. There are promotions that are not advertised. Some of these are age-related, based on where you live, if you are in the military or other public service (police, fire, etc.), or in some cases even if you are a member of a union. Not every category above has a discount on every sailing though. Check with your travel agent.
There are some good tutorials on YouTube ... just put in search term cruise prices.
summer because its better.