Even producing a black hole per year is doubtful under our current best guesses, but if one of a few extra-dimension TOEs are right (possible) we could produce them. So there's sort of no "typical" black hole produced by the LHC.

But you're right, you could make a low-momentum black hole with some probability if the numbers worked out. I don't know how to calculate what the rate would be, though - it would probably involve gory details of the particular TOE. 1 per year doesn't sound crazy, though, if they're possible.