One of the many taxi drivers in Évora will do that.
Would you know the approx cost?
That's quite a distance, and you'll probably have to pay for both ways.
http://www.rodalentejo.pt (who also run a bus from Elvas to Badajoz)
If the timing is OK, that'll be a (lot lot lot) lot cheaper, and, quite possibly, just as quick.
Based on the distance of about 22 km and a charge of around €1.20 per km on a Sunday, I would say at least €25 double that if the driver wanted paying for the empty return trip.