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.
One of the reasons that people go to Jamaica in the first place is to take advantage of the year-round warm Caribbean climate. Temperatures fluctuate little over the course of the year. The hottest months are July and August, with an average high of 90 (32) degrees and lows in the lower 70s (23 C). This differs little, however, from the coldest months of January through March, when highs hover around 86 (30 C) degrees, and lows are in the upper 60s (20 C).