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.
And it's absolutely true. This is Jamaica weather! Most of our days are filled with warmth and sunshine, even during the rainy season. Jamaica has a tropical climate with hot and humid weather at sea level. The higher inland regions have a more temperate climate. (Bring a light jacket just in case you travel to the mountains where temperatures can be 10 degrees cooler or in case you go on a windy boat ride).