Ryanair offer travel insurance policies as an add on to a flight booking, or they can also be purchased as stand-alone products. Ryanair travel insurance is offered in two levels, so you can choose the option that's right for you and your wallet.
Jamaica's rainy season coincides with ours here in Florida (I am in the Tampa area) for the most part. We have anywhere from 30-50% chance of rain daily until hurricane season is over. I didn't mean you have rain every day, all day from May to December in Jamaica, but I assume it is a lot like here in Florida.
From all the above it would seem as if the best time to visit Jamaica is during the months of December to early April (also known as the dry season). As a matter of fact, the winter tourist season (high season) in Jamaica lasts from December 15 to April 14. Christmas and Easter are the busiest weeks.