It wasn’t only lapel studs and pinbacks; bicycle manufacturers put their brand names on other items, also.
This is a type of fob for Atherton Coaster Brakes, possibly meant for keys. The back reads “Compliments of Buffalo Metal Goods Co., Buffalo, N.Y.”. Below that is the Atherton name.
1.25″ exhibitor disk with cork back for the “Western National Cycle Show” (likely held in Chicago or St.Louis).