What You Should Know
(Extracted from Jamaica Tourist Board)
U.S. Citizens travelling to and from Jamaica must present a valid passport when leaving and or re-entering the United States. Residents must present their Alien Resident Card (Green Card) together with passport of country for which they hold citizenship. All visitors are required to travel with a return ticket or onward ticket for entry into Jamaica.
For more information, go to: http://www.congenjamaica-ny.org/visas/
Valid passport or a government-issued identification with photograph, along with an official birth certificate. Canadian residents must present a Canadian Permanent Resident Card and a passport showing country of citizenship.
Also more useful information here: