According to the German Rail web site (
http://www.bahn.de/regional/view/saa...saarland.shtml), the ticket office in Saarbrücken is open on Sundays from 10:00 am to 6:00 pm. There are also ticket machines.
I don't know whether you can buy tickets on board local trains in Saarland, but I do know that you
cannot do so in Baden-Württemberg or Bavaria (with a few exceptions), so I would advise you to buy your ticket before boarding.