There is no direct route from Cascais to Portimão.
Your best bet will be to take the train from Cascais to Lisbon Cais de Sodre.
Then take the Metro Green Line to Alameda then the Red Line to Gare Oriente.
From there you can get either a long distance RENEX Coach to Portimão or the train via Tunes.
For timetables, please visit my blog at
http://barlaventostravelblog.blogspot.com/
Scroll down on the right hand side panel till you come to:
»» Algarve & Portugal - Travel Transport Links
»» Continue scrolling down in this section till you come
Portuguese Railways - 2008 - Lisbon - Algarve Faro/Lagos Timetable
or
RENEX Bus Service - Lisbon to Algarve timetable
Click on these to download the timetables from the respective sites.
