A common problem with prewar/tinplate cars, regardless of make (American Flyer, Ives, Lionel, Marx) is bent axles. If the car wobbles when it moves, one or more of the axles is bent.
Reproduction parts might or might not be available, so I prefer to just straighten the old ones.
If you have a piece of brass tube that the axle fits snugly into, push the short end before the bend into the tube for leverage, then clamp on a pair of locking pliers and bend the axle straight. The tube helps you eyeball the axle’s straightness, or lack thereof.
If you don’t have a suitable piece of brass tube, try chucking it into a drill to hold it straight while you bend the axle with the locking pliers. Just use the drill to hold the piece; don’t turn the drill on of course!
Replacement parts aren’t always easy to find. Lionel axles usually fit pre-1938 Flyer, Ives, and Dorfan. Marx axles will often fit when Lionel axles don’t. I’ve used Marx parts on post-1938 Flyer cars. Reproduction Lionel parts are available from Olsen, and Marx parts are available from Robert Grossman.
I’ve made axles out of brass rod before, using carefully measured lengths of tube to space the wheels. But if the spacing on the wheels is off, the cars are prone to derail. So I prefer to use commercial parts in this case, rather than homemade.