Currently, every ring has a Cooldown and Stamina cost that are very similar to each other. The thing is, we're running out of room there. The thought first came along when I was considering what is probably the most crowded are of design space in Rings, today: Healing.
The original thought was a High-Cooldown, zero-Stamina, Self Only Healing Ring - some kind of Second Wind, or Wholeness of Body (if you based it on Willpower xp ). I was looking for an alternative (not a replacement) to Bandage, for a soloist - removing the Stamina cost lets a solo player focus his Stamina where it's most needed. He loses the convenience of Bandage (since he's now only able to heal every 30 seconds, or so), but he gets the extra Stamina in exchange.
Converting resources (Stamina-to-Time and Time-to-Stamina both) is a generally dangerous game. It's probably best to underpower these a little bit, because the first thing players will do is try to break them. Personally, I think the low-Stamina side of the conept is more interesting than the high-Stamina, low-Cooldown side, but some of you may disagree. One important note, though: Buffs are more-or-less exempt, as their Stamina and Cooldown are both essentially negligible over their durations. This is more focused on attacks, Healing, and possibly Crowd Control/Debuffs.
One last thought: low-Stamina, low-Damage; particularly on attacks with secondary effects, like Knockback. Essentially, players don't have to pay for the damage if they don't want it. Imagine an alternative to Bump that did considerably less damage for considerably less Stamina. Would it be worth using? What about in a Range-centric build?
