Just a little more data for anyone thinking about discarding their COP ring for the second time. I had read that it took 28 days for this one (post discard) before you could get a new ring. So, I didn't bother checking the tavern door again for weeks. Big mistake.
The 28 days starts from the time you check the door not from the time you discard your ring. So, I have another 17 days to wait. If I had checked the door immediately, I'd have only 5 more days. So, if you want to change your mind a 2nd time, be sure you check the door RIGHT AWAY after you discard your ring. Check it again the next day to be sure you're on the countdown to receive your ring: it will tell you the number of days you have remaining.