Easy part to lose. Been there.... Ugh!
I would start by looking for the authorized warranty centre for Browning. Tell them you have a SA22 that needs a cartridge stop, maybe they can help you.
Western Gun Parts is a good bet. If no joy there, try Saskatoon Gunsmith Shoppe, IRCC, in Saskatoon, I got a Browning Extractor there to fix up a Norinco clone.
Other than that, phone anyone that vaguely sounds like they hang out a shingle and calling themselves gunsmiths, ask. Remember that most of the guys doing this stuff are grouchy old coots that are not altogether tech savvy and wired for interwebs. Phone. Ask for leads to used gun parts dealers relatively local to you. Gun shows are usually a good bet on that account.