The American International School of Kingston (AISK) is the most highly rated international school on the island. Their program caters to students from the early childhood to secondary education level. The school is accredited by AdvancED, and is a test centre for ETS, SAT, ACT and of course IB diploma. AISK is one of the 532 independent schools in Jamaica, 38 of which have a combined system of pre-primary through to grade-12 education.
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.