This might not suit, but if you get there and still have nothing, there are lots of car hire companies in Faro airport who work from reps on tables at the cafeteria out front. They don't have signs up , just phone, case & the cars are in the parking lot outside. IF they have spare capacity you might get a good deal. When you come out the arrivals door into the long front section turn left about 50 yards down theres a self-service with tables in the mainhall, they're usually there.