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.
Every weather report I have ever seen for Jamaica shows a 30-60% chance of rain every single day along the coasts. We had the same weather report when we went in mid-August and we got about 4 hours of total showers for the entire 8 day stay. Most of it was between 12:00N and 1:00 p.m. when we were having lunch anyway.