Like a designated driver, the designated sitter would need to be unambiguously identified. Designated drivers usually get a pin wrist strap that entitles them to free (non-alcoholic) drinks.

Designated Sitters would have to be treated oppositely. They'd have to be denied an identifying mark which would entitle everyone else to gain entrance to rides. Whether that was accomplished through a breakable wristband, hand stamp or whatever really wouldn't matter, as long as it couldn't be shared with someone else. Maybe the Designated Sitter gets to take the kids to floor shows or something...