A friend of mine found a Conn C Melody in OK condition in a church storage room. It needs some cleanup and a few replaced pads, but plays nice. It came with two Babbitt mouthpieces a 4 and 5. I don't know what would have come with the original horn. The mouthpiece caps are metal and don't really fit the mouthpieces.
I've read that the Runyon C melody mouthpiece is pretty good. I normally play alto with a Selmer C* or Otto Link metal 7*.
Just for interest sake, the serial # is 76795, which puts it in the 1921-22 range I believe. It's a straight neck.