Larry,

Usally a beach cruiser is a single speed bike. The problem you described is caused from the single front sprocket being uneven, or not centered when it is installed on the cranks. Sometimes, the center hole on the sprocket is a little too big. There are a couple things you can try. By lightly tapping a hammer on the sprocket you can try to center the sprocket on the crank. In this method you do not have to overhaul the bottom bracket. But be careful! Tapping too hard can result in a bent sprocket or damaged chain. The other option is to remove the crank arm and loosen the inside adjusting cone that holds the sprocket, and try to center the sprocket on the crank arm. The problem with this option is that the sprocket moves off center everytime you tighten it.
Very seldom is the problem caused from the rear sprocket in my experience.
Also try a serrated lock washer on the rear wheel, one that bites into the frame of the bike. This will reduce the rear wheel from slipping forward when people rent them.
Just a side note: Don't get discouraged! Some bikes are next to impossible to center the front sprocket. I have wasted many an hour trying without success! Good luck!