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.
I've been to Jamaica many times in August. Its hot and humid but when you are near a pool or beach, who cares? You can expect afternoon showers..soetimes brief (10 minutes) and soetimes an hour or so. I just see it as nature's way of telling us to get off the beach, clean up and get ready to go out for the evening. I like the summer months in Jamaica because things are less crowded yet its always a great time.