First of all, Jamaica did experience multiple slave revolts over the course of its history. The largest slave revolt occurred in 1760, called Tacky's rebellion or Tacky's war. It was an uprising coordinated by groups of slaves from the Gold Coast, called Akan slaves. Several groups rose in revolt across the island in late May of 1760. The revolt was eventually suppressed by the large white military presence on the island, and with the assistance of some soldiers and sailors stationed in the Caribbean for the Seven Years War.

It is likely not a coincidence that the largest slave revolt in Jamaican history occurred during wartime. When the slave revolt started in Saint-Domingue, the home country was experiencing a revolution in government. Ideas of emancipation and radical egalitarianism poured out of France into the Atlantic world. The change in government, and the wars that broke out helped facilitate and prolong the slave revolt that began in Northern reaches of the island spread to the whole colony. For Tacky's revolt, the Caribbean had become a war zone patrolled by French and English warships. Islands like Guadeloupe and Dominica had been invaded and conquered. In the middle of the disorder of war, the enslaved saw their chance at freedom and took it.

Tacky's revolt was less successful than the revolt in Haiti for a couple reasons. First, Saint-Domingue had an enslaved population of 450,000 (only enslaved) at the time of the rebellion, while Jaimaica at their rebellion numbered about 170,000 (enslaved and free blacks). There were simply far more slaves at a higher population density that could participate in the revolt in Saint-Domingue. Second, the home country (France) was in utter turmoil during the revolt in Saint-Domingue, and the prospect of abolition was actually being talked about, if only by the Amis des noirs. That idea was never even considered by the colonial or British government. Further, the presence of Maroon soldiers in Jamaica limited the influence of the rebellion. Maroons maintained their sovereignty and independence from the colonial government on condition that they assist in capturing or returning runaway slaves, and by not sheltering rebels or fleeing slaves. The Maroons did not consider "racial solidarity" as important, instead they looked after their own interests and failed to support revolts. There was no serious Maroon presence in Saint-Domingue occupying the mountains, and the enslaved were able to flee west and south to maintain the revolt.

It is also worth noting that Jamaican slaves rebelled at other times in their history prior to the Haitian revolt. There were rebellions in St. Mary's Parish in 1765, Westmoreland in 1766, and Clarendon in 1690. These revolts were not as large or coordinated as Tacky's revolt, but they were a known part of the islands' history.

EDIT: Going back over my files, I found a comprehensive list of Jamaican slave revolts before 1780. Amy Marie Johnson's Ph.D. at Duke, 2007: "Expectations of Slavery; African Captives, White Planters and Slave Rebelliousness in Early Colonial Jamaica"

1669 - Uprising on Col. Sutton's plantation. St. Dorothy Parish

1673 - 200 slaves, mostly from the Gold Coast, in St. Ann's Parish

1678 - Rebellion in St. Catherine's Parish with others implicated.

1685 - Insurrection staged by a slave named Cophy at Guanaboa Vale

1690 - 400 Gold Coasts slaves rebelled at Clarendon

1696 - Revolt on the estate of a Captain Herring

1720 - Revolt on "Downs' Plantation" who eventually settled in the mountains

1742 - Coromantee rising in St. James' Parish

1760 - Tacky's Revolt

1766 - Coromantee rebellion in Westmorland

1776 - Hanover revolt