IIRC Numrich had 22 Johnson barrels for the M1 carbine a couple of years ago. For a while it was a pretty popular cartridge/gun combo. If you look around I'm sure you can find some brass, dies, etc, maybe even some loaded ammo.
It's really a pretty good concept. The original idea was to sell the idea to the Army (always a good idea to target a customer who buys in BIG volume) so they could convert the millions of aging guns and buy new ones from companies that had fully amortised tooling. While the 5.7 Johnson doesn't have the power of the .223 out of a 20" barrel, I'll bet that a little carbine shooting it is pretty close to what an M4 with the 14" or even the 12" barrels you see these days will do. Give tne length of an M4s buffer assembly, the 18" barreled m1 carbine with the side folder is probably more compact than a 12" AR type gun. The M1 carbine was arguable pretty close in concept to what the "new" PDW weapons are. If they had adopted the 5.7 M1 carbines back in the '60s it would have been just exactly what FN and others are hocking today, just 50 years earlier.
As a light, handy sporter for small game/vermin it's a darned good package. That cartridge with the right projos in a bolt action or a single would be pretty fair coyote medicine.