If you are looking for good weather with reasonable rates, November to mid-December is the time to consider. After that, high season rates kick in through mid-April, when the weather is at its best, with high temps averaging from the low to mid 80’s. Summer is the cheapest time to visit, for reasons you’ll discover as soon as you step off the plane into the heat and humidity. Look for highs then in the high 80’s to mid 90’s. Jamaica has two rainy seasons, May-June, October-November, but it can rain briefly at any time. Rainfall is greatest on the northeast coast of the island, around Port Antonio, which is what makes the Blue Mountains so green.
Here is the Jamaica Meteorological Service report on current conditions in Jamaica.