It's a lot like Florida's. Rain generally starts to slack off the closer into winter you get. It's really nice for the most part between late Oct. until late spring, when the daily showers start. But look at this year! There's a hurricane right now & south Florida has had LOTS of rain the past couple of weeks, when it usually starts to slack off a little by now. So you can never be sure. By mid June you will certainly have at least one shower a day. By Aug. & Sept. you are likely to have even more. Most of them don't last that long. The ship sails in and out of rain frequently. Now it also depends upon what you call the Southern Caribbean. Antigua & Barbados areas are one thing. Aruba & Curacao, etc., might have a little different pattern. Go to MyTravelCo.Com and they have a weather section over on the left side of the page, I believe. Maybe there will be info. there. You can also look in travel books (like Frommer's Guide to the Caribbean) & they often have avg. rain amounts, etc. So do AAA guides. (Yes, they have them on the caribbean, too.)
I take a cruise every Thanksgiving week. I have encountered about 10 minutes of rain in St. Thomas twice. Both times a huge rainbow covered the island. It generally is good weather unless a tropical wave or depression is around.
We were at St. Thomas on 11/3 and had a down pour for about an hour at Sapphire Beach. It didn't even rain at Maegan's Bay. When we returned to San Juan, Puerto Rico, they had had pouring rain for 72 hours with flooding. You never know.
Bon Voyage and Happy Thanksgiving.