How about a maypole? Or a slow race. Maybe an egg race, where two by fours are placed on a. Side by side course to drive over while holding a spoon of
Choice with an egg in it.
Hang an old toliet seat from a tree branch in a field you can drive through, then every car get a roll of paper. The passenger has to throw the roll through the seat without the car stopping.
Line up a half dozen Model A's. Place drivers in a circle with Blind folds on about 20 metres away from the cars. A navigator from each vehicle stays with the car and when they get the signal they start blowing the horns. Each driver to locate his car by the sound of the horn. No spoken instructions allowed. Stand back and let the fun begin.
Hang a golf ball from a string on the front bumper. Set up coffee cans a go golfing. Every time the driver gets out to see how close he is, it's a stroke.
Take a look at the MAFCA website where there is a book of car games available for download. You need to be very careful in selecting games as many of them used in the past will violate insuarance coverage. The MAFCA book includes only the "safer" games.