I've been workshopping a Boxer/Puglist-esque fighter subclass for fun, and I was thinking of providing some kind of feature like a KO punch, where if you crit on an unarmed strike you can force some kind of CON save from the opponent or else they're knocked unconscious. 

My main problem is that I don't know whether it would really ever be relevant, since crits are obviously uncommon so it wouldn't come up often. I was wondering if there was a better way to implement it or if it was fine as it was, so if anyone here has an idea for it or changes that would work better I'd appreciate it.

Well, I like the KO on a Crit idea. It fits and it feels appropriate. Remember, unconscious is a pretty sever condition to impose, even for just a round or two.

What you could do is base it off of something similar to the Monk’s Stunning Strike. Give your subclass a limited pool of uses for the ability where you force a Con save and on a failure they are stunned for a round, but if they fail by 5 or more they fall unconscious for a round instead.

If I were to implement the K.O. on a crit, at what level should the feature be given? I have features for 3rd and 7th, so it'll either be 10th, 15th, or 18th.

Seems reasonable for a 10th level feature. It’s powerful enough to rate, but will be uncommon enough not to be OP. Depending on what your 7th level feature is you might even use this as a supplemental feature at that level.