What counts as a "hit" for the new affix on Broken Promises?
I did some testing earlier today and found there does seem to be a bit of an internal cooldown. After 3-4 seconds of your crit chance buff going down, you can repeat the process of activating the ring.
I play monk and tried with a few spirit generators and none of them seemed to be a clear cut best choice, although I do need to keep testing. To answer your question about hundred fists (and each spirit generator), they are all combos with 3 hits. So even though it shows a lot of little punches, it only counts as 3 hits per sequence. Hundred fists is cool though, because your ring buff activates right before the 3rd part of your 2nd sequence which is a flurry of little punches. As long as you didn't crit in the middle of it, that is.
Bonus: I did a little more research and it seems that only skills performed by you will count towards the ring proc, so pets/item specials probably won't affect it. But sweeping wind does proc it...and it can't crit ;)