I've been researching this quite a bit. The players are molded to that rod since they are telescoping (an inner rod that slides inside). if there was a pin, you wouldnt be able to slide the inner rod through.
Bonzini and Rene Pierre have men that are clamped around the outer rod so I guess theoretically, if the rods are the same diameter, you could somehow remove the plastic molded man and replace with a bonzini or rene pierre man. or replace the whole rod.
if you live in the US let me know where you find telescoping rod sets cause that is really difficult.
all that being said i have an unidentified italian table and bought a replacement rene pierre rod to see if it will work. ill update this thread with my findings.