The holes on my rotary phone are about 1 cm. One can make them nested, since it would have to be custom anyway: starting with the diameter of, say, 3 cm, adding a bit more than 1 cm on each side (3 cm, 4.5 cm, etc), and assuming that at least floor (pi * (1.5 + 2.5 * n - 2) / 1.5) keys fit in the nth such nested ring (1.5 + 2.5 * n is the outer diameter, - 2 is there since the holes won't be on the outer diameter, / 1.5 cm is to leave some space around them; that's not meant to be optimal, just a quick estimate), that'd yield 101 holes/keys with 6 rings, with the outer diameter of 1.5 + 2.5 * 6 = 16.5 cm for the last one. That's a rather small keyboard.

Edit: nested rings would also work for modifier keys.

Edit 2: fixed the formula.