To get from Faro to Viana de Alentejo is not that easy.
You cannot book through tickets.
The Sector Evora - Viana de Alentejo is operated by a local bus company and according to the local Council, buses only run on this route Mondays to Fridays.
See:
http://www.cm-vianadoalentejo.pt/pt/conteudos/informacoes+uteis/transportes/
Operated by Rodoviária do Alentejo - Line 8146
Departures from Évora: 07h15 - 17h30 - 19h15
Departures from Viana: 06h49 - 08h10 - 19h55
Services depart from Evora Bus Station
For the sector Faro to Evora one has two options:
1) Bus:
Service operated by Rede Expressos - http://www.rede-expressos.pt/0010.asp
Current Timetable as follows:
2) Train
Portuguese Railways www.cp.pt operate two services a day between Faro and Evora with changes in Funcheira and Beja.
Current Timetable as follows:
Dept. Arr.
Faro 9h05 Evora 14h24
Faro 13h08 Evora 17h41