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.