I'd also prefer not to see the Ring of Favor and protection, unless stamina boosting gear is available in other forms as well.
The third ring I'd like to not see a return of is actually the Rusted Iron Ring, it's a bad concept because of how limited it's uses are.
Here is rings I'd like to see added to the game.
A ring that makes your rolls take half as long, and go twice as far, but removes all invincibility frames. Mobility sans Invincibility, a dangerous, but game changing utility trade. Potentially of use by Fat Rollers, or even Dark Wood Grain Ring ninja's that are in a rush.
A ring that makes you take 80% less damage from all sources while below 20% HP: Pretty much a Blue Tearstone that actually... works?
A ring that directly increases your shields stability by 10%, or makes weapons bounce off your shield in PvP, etc. Call it Guards Ring or something.
A ring that alters the damage type of your attacks: from slash to trust, or thrust to crush, for example. I'd also like to see the 3 types of physical damage actually vary in their effect a little, so far the only special one is thrust because of leo.
A quick ring that makes your attacks/spells twice as fast, but reduces AR by 30%, and you inflict 0% of the original poise damage value. This results in attacks that aren't capable of breaking your poise threshhold, but come incredibly quickly, and with a net increase in damage. The 30% AR loss should also effect buffs to avoid this being a required ring for buff builds.
Anyway, just my two cents.