Tightening the bolts on training wheels for a child's Schwin bike
Simple answer - do the bolts up tighter.

Bolts for training wheels are pretty hefty, it's hard to over tighten them with a hand wrench. 

If you don't have a suitably long wrench that will allow you to get the torque you need, you can extend the wrench handle with a length of metal pipe. Avoid using an adjustable wrench as these can round the bolt heads off. Not everyone has a length of pipe laying around of course. Any good bike shop will tighten the bolts for free or a nominally low charge.