Maybe they blindfold him.
Blindfold each student, spin him in circles, and give him the opportunity to pin the mustache on the paper target.
He continued to play for over 10 minutes with a medley of Super Mario Bros. music, though he shed the blindfold after the first song.
These could include a bottle, pacifier, bottle brush, bulb syringe, thermometer, nail clippers, pacifier holder, booties, etc. Blindfold the mom-to-be, and watch her try to guess each of the items as she picks one up out of the bag.
Have each guest put on a blindfold (that should have everyone giggling!); one that's impossible to see through.