Brad-
Let me start by saying it’s been 25 years since I worked in the Caribbean so, that said, I obviously have very little in the way of contemporary knowledge. With that caveat let me make a few suggestions.
First, when shooting in the Caribbean it’s best to lower your expectations and/or plan on bringing whatever you’re going to need with you. The chances of finding anything on Grenada are minimal at best. The closest large city (well kind of large) is Port of Spain, Trinidad. The next closest city is Caracas, Venezuela. Since it’s unlikely that you’ll find much by Googling ‘Video or Film Equipment Rental’ you might want to start by calling the TV stations in the area and see if they can recommend any sources — potentially including themselves — for the gear you’ll want. But don’t be surprised if all you’re able to source is C-stands.
Considerably up island is San Juan, Puerto Rico. You may have some luck there, but the shipping charges are going to be higher because of the distance. Back in the day the source for almost all serious film and video rental for the Caribbean was out of Miami. That may still be the case, but I don’t claim to know.
Getting back to bringing your own, if you want a dolly consider bringing one of the smaller/simpler ones. For example we have a Losmandy Spider Dolly that I’ve shipped to several locations domestically. The flex track and dolly weigh something around 45 pounds so the FedEx cost is quite manageable. Of course shipping internationally adds a whole new level of cost and paperwork so you may be better off paying excess baggage fees and clearing your stuff through customs yourself. Speaking of which be sure to obtain the necessary carnet paperwork to facilitate taking gear out of the country and back.
Best of luck and hope some of the above helps.