Car rentals in STT have been a hot mess with the big uptick in visitors. If you check out the TripAdvisor forums you can read some of the threads. Vehicle shortages and visitors not being able to locate something to rent are common (booked out months if not a year in advance). Some people with the traditional big rental companies wait hours for their car at the airport or are told their rental can’t be fulfilled.

Paradise, a local company, meets you at the airport and then will pick up the vehicle at the marina for an up charge. They likely won’t have anything available at such short notice but it is worth a shot.