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.
Here's some information regarding Jamaica weather. Rainy season' begins in May or June and extends through November or December, with the heaviest rains in September and October, Rain can fall at any time of the year, however, and normally comes in short heavy showers, often followed by sun.