Ah yes! It was called "Being Deputized." They still did this in the late 1980's- early 90's. I have probably 30 or more in a plastic Tupperware box. My parents probably have the box at their house, so I can't really answer your question on rather or not it actually said Silver Dollar City on them, my guess would be that they did though.
Those little Deputy pins that the Sheriff would pass out, became an SDC staple for my family as much as the collection of dip-your-own candles from Carries Candles in Midtown.