No, it is not possible to take a train from Faro Airport to Cabanas Tavira.
Trains run from Faro Town Station to Tavira. You would need to take a taxi or the infrequent bus from Faro Airport to Faro Centre.
You will find a bus timetable for the service from Tavira to Cabanas here.
http://thomasallen.home.sapo.pt/travel/029.htm
For Cabanas, a hire car is recommended.
