I am based in the Algarve in Portugal and am not fully conversant with hire car availability in Seville.
If your are planning to do a one way trip between Spain and Portugal you should use one of the majors such as AVIS/HERTZ/EUROPCAR. Be aware that their one way inter-country drop charges are generally exorbitant.
If this is a case you may wish to us public transport to travel from Seville to Faro and hire a car there.
If you are doing a return, Seville - Faro - Seville, from previous visits to Seville, however, I am aware of two car hire companies with offices just outside Santa Justa Train Station in Seville:
These are:
Atesa - http://www.atesa.es - They have an office just near the station on Avenida Kansas City.
Auriga Crown - http://www.aurigacrown.com/ - Avda. de Kansas City, 32.
Again near the train station.
