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 climate of Jamaica. The island of Jamaica has a tropical savannah climate or a savannah climate with many sunny days. However, there is a reasonable chance of (very heavy) rainstorms or thunderstorms. During the day temperatures are around 24-25 degrees Celsius on average.