Absolutely, no need to go to Faro.
Firstly, see the following articles on my blog about getting from Lisbon to Portimão.
http://bit.ly/6THxpM
Secondly, Alto club is actually closer to Alvor than Portimão. It is quite a distance from both the train station and the bus halt.
There are few downtown car hire agencies left in Portimão. Most have migrated to Praia da Rocha.
Renex Bus Company operate at least 8 buses a day from Lisbon to Portmão and Praia da Rocha.
Rede Expressos bus company operate at least 5 buses from Lisbon Sete Rios Bus Station to Portimão and Praia da Rocha.
Links to these Bus Companies can be found in the right hand panel of my blog.
I would suggest that you get a bus from Lisbon to Praia da Rocha. Pick up a car there.
Avis, Hertz and several other companies have rental offices along the strip there.
You could try these guys also:
http://www.autocarhire.net/index.php
Note: Although there are buses to Alvor, I would suggest that Praia da Rocha is a better place to pick up the car as the agencies are all within a fairly compact area.Also, bus is a better way to get down to Praia da Rocha from Lisbon than train as Portimão station is a ways from Praia da Rocha.
