Not exactly what you're asking, but I'll talk about slave diet in sugar producing northeastern Brazil, which could shed some light into the probably similar practices in the Caribbean.

Leaving Africa, Câmara Cascudo tells us that the slaves were given a bag of provisions, mostly composed of fresh or baked corn or manioc flour (bought in the Brazilian ports). In their march, they were sometimes given dried fish as well. Disembarking, the scurvy ridden slaves were fed cashew apples, to help them recover. This recovery period was very important for the slave traders, since the landowners looked for healthy slaves. Further South, in the Fluminense coast (Rio de Janeiro's coast), they were fed with manioc flour, beans and jerky for the same purpose.

In the plantations, they cultivated Bananas, Nham, and Manioc for feeding the slaves. The "engenhos" (sugar plantations) were mostly self-suficient and fed their own workforce.

According to Cascudo, the basic slave meal was essentially the same, to which sometimes it was added some fish or meat. This base consisted mainly of Manioc flour in the North and corn in the South.

"A slave's meal in a rich farm is composed of corn, black beans, bacon, jerky, oranges, bananas and manioc flour. (...) It is allowed, however, to a malnurished slave, to spend the income from the sale of his grown vegetables into buying bacon and jerky. Finally, hunting and fishing, practiced in his free time, allow him a more wholesome diet". It is important to clarify, however, that all the slaves' expenditures were made in the plantation. Therefore, when Cascudo is saying that they "bought" food, it means it was from their own master.

Finally, it is interesting to notice that many African plants were brought to the American continent with the objective of feeding the slaveforce. It is the case of the "Dendê" Palm tree, whose oil is still used in many typical dishes across northeastern Brazil.

The point is: a plantation didn't need to only produce its main export crop. It was feasible (and economically efficient) to have the slaves also plant food crops to feed themselves and their masters.

Source: Luís da Câmara Cascudo - História da Culinária do Brasil