Your best option would be by bus.
Please see these articles on my blog from last year. This deals with a trip from Lagos.
http://barlaventostravelblog.blogspot.com/search?q=Fatima
Alvor is between Lagos and Portimão and in my opinion your best bet would be to get a taxi or local bus into the centre of Portimão where you could connect with the services quoted.
I have published a copy of the relevant timetable on my blog here:(click to enlarge)
There is a direct bus service to Lisbon from Alvor operated by RENEX. However, this terminates at Gare Oriente and does not provide convienent connections to Fatima Services which leave from Sete Rios.
Trains are not that easy either as you have to transit Lisbon and disembark at Caxarias, 10km (6 miles) outside Fátima. There are only a few buses a day between Caxarias and the Sanctuary.
The only other means of transport would be by car. If you took at hire car, you should be aware that the main routes are toll-motorways.
Fatima lies about 350km North of Albufeira, in the Algarve. Alvor lies 50km from Albufeira via the A22 motorway. Total distance is circa 400km each way. If you have a car you can do a long day trip as follows:
- Follow the signs from Alvor of the A22 motorway
- Turn right onto the A22 motorway in the direction of Faro and Espanha.
-After +- 60km head onto the E01 / A2 / IP1 motorway toll road in the direction of Lisbon
-After 2 hours follow the signs for the A13 Santarém
-On arriving in the Santarem Area, head onto E01 / E80 / A1 / IP1 Motorway.
-Continue until you see the off-ramp for Fatima.
-Exit for Fatima.
