According to law on the island, non-Jamaicans must apply for work permits, which are dealt with by the Minister of Labour. If you are a citizen from a Commonwealth country, this can be done after arriving but, if this is not the case, your application must be completed prior to arrival.
You can find a search engine for jobs in Jamaica here, although bar work and helping out in the tourist trade are the two obvious choices. Should you feel more altruistic though, volunteers are always needed in the Blue Mountains. Global Volunteers have run a scheme for many years now, where workers assist in repairing and building villages and generally give something back to the island.