Our favorite time (and everyone else's) is November-April, but Jamaica can be very crowded then. The temperature is fairly stable year-round, so it's possible to visit in other months as well.
Winter coastal-area day temperatures are in the 70s-80s F/23-32 C. June-September is usually in the 80s-90s F/30-35 C. Nights tend to be 5-10 F/3-5 C cooler everywhere. Temperatures in the hills and mountains are usually cooler than on the coast—take a sweater for nights.
The hottest time is July-October, when the humidity, heat and hurricane possibilities are the highest. Most rain falls May-October, but even then it generally comes in brief showers and seldom ruins anyone's vacation. Hurricane season is June-November.