Brace yourself - this is not normal.
I have an old 22" rim (37-501, 22x1-3/8) and all I can get is skinny tires for it. But I'm an idiot and I really want a wider tire on that rim. I want it so bad I am grasping at straws for ideas.
So here's the thought:
Get a new tire (22x1-3/8) Get a new BMX 22" tire (which is NOT gonna fit my rim)
Cut the skinny one's beads off with about 1" of rubber above it. Cut the bead off the BMX tire very low.
Glue BMX tread to old-school beads.
Viola! a 2" wide tire for the old 22" rim.
Yeah, I know this is nuts. But CAN it be done and become whole again?
Maybe, just maybe, someone here knows if this has ever been done. Please let me know.