I think there is an outside chance you could get Bob Stoops after this season. He's getting long in the tooth at Oklahoma and might want a change (seen more than one column proposing him for Michigan). But I'm not sure even he's really an upgrade. Even with nothing like the recruiting challenges he'd face at Notre Dame (the man picked up Dorial Green-Beckham. Imagine that happening in South Bend?), he's struggled to compete with the new Big 12 powers that put significantly less recruiting stars on the field every Saturday. No kid, either.
More realistically, your best bets are experienced guys from second-tier programs, like David Shaw, Pat Fitzgerald (right...), Nuamatolo from Navy, the guy from Wisconsin, Mark D'Antonio maybe. All fine coaches. But no reason to think any of them are better than Brian Kelly - who by the way handles many aspects of the job (recruiting, program-building, the endless media obligations) way better than we have any right to expect.
Kelly needs to clean some things up. For sure. But he's earned the time to do so. Like I said above, I think the bigger risk is he leaves for another job while we sit around debating whether he's good enough for us. Then we're really F'd.