I've been waiting for someone to do a PIC programmer made from an Arduino. There's no particular reason that this should be any more difficult for a modern PIC (with low-voltage programming) than the ArduinoISP for programming other AVRs.
However, the pic16C56 is NOT a "modern" PIC. It needs the equivalent of high voltage parallel programming, and it's not even erasable (It's a "one-time programmable", unless it also has the transparent window for UV erasure.) Unless you're really sure that it's blank, it's not useful for much beyond sculpture.