The temperature varies little through the year in Jamaica so no matter when you go it's going to be about the same. Many sites on the internet can give you climate info, google Jamaica weather info or Jamaica temps or any other phrase and you'll get more than you need. You'll be plenty comfy in May or June though.
I have been to Jamaica in the months June, July, August, and September over the past 5 - 6 years. The temp varies little from month to month, but does seem to be more humid later in the summer. No worries, its all good. We are going in early May this year, so well see what it is like then.
We love the weather in June. Hot and sunny daytime, nights are quite warm as well. Never needed a sweater or any thing else during the evenings. Some nights it is quite warm and humid, most nights are comfortably warm. But I love the heat of summer, always have. Pack light weight, summer clothing, you won't need anything more.