I don't know much about Jamaica, but I do know that off-season for tourists is the summer months here - June to September. We have gone to Mexico twice in the summer, and got WAY WAY WAY more "bang for your buck" - most recently, two weeks for less than half of one during tourist season! So we will be getting married during the summer in the Dominican. I am sure it is the same in Jamaica.
A word of warning: summer may be cheaper at all of these places, but it is REALLY hot. I know it is always hot in those tropical places, but this is when the year highs are, and the temperature really does not drop that much during the evening. Also, it is rainy season, but it is probably not going to rain all day every day anyway. On our recent Mexico trip (maybe Jamaica is different?) it rained at night, and only once during the day during the two weeks.
So anyway, we have found that is a good way to save some money.