Why do we think that there is no two-solar-mass black hole?
As you said in your question we only know about Black Holes creating in Super Novae, which lead to relatively big BH. The reason they can't be smaller in these cases it that they are created when the core of the star reaches a critical mass that overflows both the electron and the neutron degeneracy. Lower masses can be hold by those degenerate mass states and won't collapse any further.

Theoretically BH with masses less than the solar one could exists if there was some method capable to compress it's mass reaching radii smaller than their Schwarzschild radius.