Try this. Hard boil an egg, mash it up and put it with the ring for a couple of days. A bad egg would be even better. Eggs are high in sulphur and hydrogen sulphide will be produced as the egg breaks down. This will create a patina on the silver.(Please let me know if this works.)
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LOL. I posted that as a totally speculative method which should work. I've just had a google and it looks like other people have done it successfully. Clean the ring first to get any oil or grease off it, then do the mashing in a plastic bag to prevent mess. Keep the bag sealed when the ring is in there to keep the gas in.
AndyG, you're just full of good answers today. I didn't even think about the sulfur and hs in an egg. Good answer.
I believe if you store it with stainless steel it will get a patina more quickly.