I assume you have already explored much of the online resources on Mexico gardening and even tho Cozumel has a very different environment much it might still apply?

And that you know that since importing seeds and plants is going to be heavily restricted by customs you may be dependent on what seed crops you can find locally. Corn obviously, local varieties of dried beans, peppers, tomatoes, and squash.

I'd also suggest contacting the various universities that have agricultural programs for information on irrigation needs, fertilizers, planting dates, etc.

I did find one publication titled "VEGETABLE GARDENING IN
THE CARIBBEAN AREA" I linked below (although it is dated 1967). Be patient, it takes forever to load.

Good luck with your project.

Dave

Here is a link that might be useful: Vegetable Gardening in the Caribbean

If it is limestone, it is basically the same mother rock as Yucatan, so take a ferry and go look at the markets and buy seeds on the mainland. Not sure how close a seed store will be, the area is a tourist trap, but there are numerous villages on the road to Merida, you should not have to travel far. On top of what Dave suggests, chayote, malabar spinach, amaranth, eggplant, sweet potato, okra, watermelon and melon should all be available and easy, some in the rainy season, some in the dry season.