I go every June. It is hot and humid. The rain is the big variable. Mostly its just an hour or two later in the afternoon. Last June, the first week it rained at least 4 hours every day for 6 days in a row. But, that can happen anytime.
I like June because it is dead quiet in Negril and it is very laid back. Also, the air and hotels are MUCH cheaper in June.
