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.
The other months, also called the dry season, have much less rain and humidity. Of course you all know there is the chance of a storm during the hurricane season, which starts in June and peaks from August to early October. Its always warm/hot in Jamaica but is cooler from December to April.