The Hillel Academy is credited by the SACS/AdvancED in the United States. The school was founded in 1969 by the Jewish community of Jamaica as a non-denominational, independent, co-educational, multi-cultural school. It is comprised of a Preparatory School (age 3 -11), a High School (age 11-16) and a Sixth Form (age 16-18). The school features the IB Program.
There are a few other options listed in the Expat-Quotes article on International Schools in Jamaica.