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.
There also is a reasonable chance of completely gray, wet and windy days. However, Jamaica doesnt really have a real rainy season with rain for days on end. Most of the rain falls during the months of May-June and September-November. The amount of precipitation depends on the location and the altitude you are in.