Jamaica will let you stay up to 180 days without a VISA authorizing longer. However, the maximum you can get stamped at the airport is 90 days. That forces you to go to Jamaican Immigration to ask for an extension if you want to stay longer (up to another 90 days). Be nice when you ask as they don't have to give you one. I don't know for sure but I think that costs $10,000 Jamaican. May be more now with the devaluation of the Jamaican Dollar. Let's see what others say.
Peace and Guidance