If you are arriving at Faro at 22:00, you will be going through Albufeira station en route at 21:34 according to the summer timetable.
Why not get off there and arrange for someone or a taxi to pick you up from there.
Faro to Albufeira is 30'km and you will be charged +- €50 after 21:00 to go from Faro to Albufeira.
As regards booking taxis in advance this can be difficult if you don't speak the language.
There is usually at least one taxi at Faro station most of the time. Albufeira Station is at Figueiras, 7km from Albufeira. There may be a taxi there - there may not.
If you are staying at a hotel or an agency arranged apartment, I strongly recommend you ask them to arrange for a taxi to meet you at either station.
