An article in the Observer says that the Maypan variety is well suited to Jamaica and is wind and rain resistant.

This link has a lot of good information on growing coconut trees. It looks like there could be disease, too much/too little water or soil/nutrient problems.

I don't know the planting method you used but this article says:

In low-lying areas, beds several feet high and wide should be constructed to prevent waterlogging of the root zone during wet periods. In some areas a hardpan in the soil profile may need to be broken up and mixed with topsoil prior to planting. In the rocky calcareous soils of Miami-Dade County, rock plowing to a depth of 6 -8 inches (15 - 20 cm) and trenching about 16 - 24 inches (41 - 60 cm) wide and 18 - 24 inches (45 - 60 cm) deep is recommended.

It seems like the yard gets flooded some, so that could be the problem?

http://edis.ifas.ufl.edu/mg043