Originally Posted by Jeff Wills

Yes, the Schwinn size was 20 x 1 3/4" while BMX-ish tires are 20 x 1.75"... and they don't interchange. Bicycle tire sizes are weird.

You can install 20 x 1.75" wheels pretty easily, but I'm not certain that alloy rims with coaster-brake hubs are available. No doubt someone will point to some. Also, the fork accepts a 5/16" diameter axle while most "BMX" wheels use a 3/8" diameter axle... at least they did when I was working in a bike shop (40 years ago...). A little work with a file will enlarge the slots enough for the larger axle.