If you can find one, the Cleveland C vintage cornet mouthpiece is very nice. The shank contour seems to be unique for that era. I have two of the mouthpieces and the only difference is the rim. I also have a H. N. White C mouthpiece and it is slightly different with a smaller bore size.
FYI, I also have Cleveland mouthpieces for trumpet and euphonium/baritone that work very well too.
I also have a King 7M cornet mouthpiece that is simply fantastic. I have it loaned out to a friend. These are much harder to find that the Clevelands.