ozman, if you don't already have it you might want to get "Bobo's modern book of coin magic". It is slmply littered with great ways of vanishing coins (or in your case rings).
Two popular ones that spring to mind are the "retention vanish", and the "french drop" - If you learn these I promise you you will not regret it. They will be useful for so many things. I adit it's going to take some practice - but tthen we all must suffer for our art
Alternatively - check out my routine with Yankee Toms "Dis-Cord" (now reduced to £9.90 at
www.emagictricks.co.uk ). You have to palm the ring at one point - but you have (imho) a good mis-direction going on - which should make it much easier.
http://www.talkmagic.co.uk/viewtopic.php?t=1875