I believe your best bet would be to travel by train to Reus and then
take a taxi or bus to Salou.
According to www.renfe.es, a train leaves Madrid every evening at 10pm
and arrives in Reus the next morning at 4:50am. You can purchase
tickets online at the Renfe website.
From the Reus train station you should be able to take a taxi - to
Salou the journey time will be around 30-45mins and will probably cost
in the region of 25 euros.
I believe there are also buses from the centre of Reus to Salou, but
they may not run that early in the morning.
Roger.