you need to google work permits in Jamaica and while you are checking that out google getting married to a Jamaican citizen. Their laws change all the time so it is best to get off the internet. Also once you are there you can check things out a little easier.
I do believe that if you marry there and then apply to stay it is somewhat easier and by being married you get the right to work. You have to have many documents to take to Kingston to begin working on your papers. You will find out what these are when you google (passport, birth certificate, marriage license, health certificate, police report , financial papers, etc) Here is one site I found http://jamaica.visahq.com/ and I am sure if you google you will find your answers.
Good luck...remember things in Jamaica take 3xs longer than in the states and traveling back and forth to Kingston several times is also costly. Also often there are fees associated with each application which you should be made aware of.
Let us know how you come out.