The DR, falls into Zone 10-11, some berries require a minimum amount of cold days before they will produce fruit. ( Blueberries, Rasberries etc.) although there are some varieties that need very little.
Cherry, and/or Cherry type fruits that can or do grow well are:
Barbados Cherry ( these are easily found all over the Island ).
Cherry of the river grand ( aka Cereza Brazileño )
Grumichama, although it taste more like a grape, does grow well here.
Jaboticaba also can grow here, also taste a bit like a grape.
and finally :
The Capulin Cherry I attempted to grow from seed, it sprouted and was doing ok, but, turned brown, Since I had no cultivation information on how to start from seed, who knows what caused it to die, maybe it was the heat, or too much water, or maybe It needed to be transplanted into the ground. I feel that the Capulin could grow here in the DR.