Your chances of finding a rental guitar are somewhere between abyssmal and non-existant in Road Town. I vaguely recall
having seen an acoustic guitar for sale
at one of the stores that sells everthing from kitchen appliances
to nuts-and-bolts in Road Town. I can't recall
the name, but it is just off the main roundabout. You could also try checking out the BVI
forum on TTOL as there are quite a few BVI
residents there who might be able to point you in the correct direction.