Have built a few PK2 clones and programmed many chips without a problem, if yours has a Pic18F2550 chip then cannot see why it should not work.
Can you specify / link any details of your PK2 ? or do you know if its program is Microchips firmware V 2.32 ?
I programmed a 1938 just last month - all ok, would be very surprised if your Pk2 clone would not program it.
You can download Pk2 V2.61 from here, at the very bottom of the page.
https://www.microchip.com/development-tools/downloads-archive