You will only be able to do this with one of the big companies like AVIS, Hertz and Europcar and I suspect that the one way fee will be substantial as the rental will be between countries. I had some kiwis last week who rented a car in Valencia and dropped it of in Huelva and then took the bus to Faro as they could not get a good deal on cross border one way rentals.
Many others have asked the same! :))))
The bus is your best answer. Then pick up a car in Faro.
