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.
Jamaica averages about 80 degrees year-round, so climate is less a factor in booking travel than other destinations. The days are warm and the nights are cool. Rain usually falls for short periods in the late afternoon, with sunshine the rest of the day. May through December gets the most rain--September and October in particular.