Thanks for asking first. As with virtually every country, Jamaica takes working here very seriously and working (or volunteering for that matter) illegally can get you deported and not allowed back on the island for a year or more.
The process takes about 5 weeks and the fees to apply and obtain a work permit for a couple months would be around j$43,000 - and then there is the costs of going to Kingston and getting the actual permit. Add another couple hundred us$ for this and you are looking at a cost of well over us$600 just to obtain the work permit for a couple months.
And of course, you would need to be providing a service that a Jamaican is unable to perform for the business you are planning on working. There would have to be a job notice placed in the paper offering the position to qualified Jamaicans first and only if there are no qualified applicants would you able to be hired. You really have to have some special skill the island needs to be able to get a job here. Taking a job away from a qualified Jamaica is not only illegal, but will win you very few friends because it is highly inappropriate.
Contrary to what some people think, volunteering here is also subject to the same guidelines. If you are volunteering with an established, legal charity, that is fine. But to volunteer to do something that could be a paying job for a Jamaican can get you into equal trouble with immigration, subject to deportation and being banned from returning to the island.