Firstly, you do realise that Porto is in the North of Portugal and by road 556 km from Faro. By car its about about 5 hours and public transport between 6 and 10 hours travel.
There are no direct bus or rail services from Porto Airport to Faro Airport. You would need to get the Metro into Porto and from Faro probably take a taxi to the airport as the bus service between Faro town and the airport is infrequent.
As you are staying in Alvor, the coach operator Renex.pt serves the town centre from Lisbon.
The itinerary would be as follows and allowing enough time for you to get the Metro into Porto Centre:
Dep: Renex Depot - Porto 11.00
Arr: Renex Depot - Gare Oriente Lisbon: 14:30
Dept: Renex Depot - Gare Oriente Lisbon: 16:00
Arr: Alvor 19:05
Cost would be Euro 26.00 per person one way, based on current prices,
The are other permutations but the would not be much faster and probably a lot more complicated.
You can find direct links many rail and bus timetables here in Portugal route on my blog:
http://barlaventostravelblog.blogspot.com
Scroll down on the right and you will find at panel entitled:
»» Algarve & Portugal - Travel Transport Links
The Renex Depot in Porto is situated at:
Campo Mártires Pátria 37,
Porto.
You would have to get a Metro from the Airport to Porto São Bento and then walk/cab the 400 or so metres to the above address.
Note should arrive at the Bus Station at least 30 minutes before departure to buy your ticket. Tickets cannot be bought online.
