It appears that only the original Karate Champ core exists currently.
I was wondering if a core for Karate Champ - Player vs Player would be possible? I believe both games use the same underlying hardware.
Has anyone seen anything regarding possible development on this core?
I'm neither a Karate Champ expert nor a heavy user of arcade cores, but I think it's already supported. My system has "Karate Champ (US VS version, set 1)" through "Karate Champ (US VS version, set 4)" as well as "Taisen Karate Dou (Japan VS version)" under "Arcade/alternatives/Karate Champ".
Thank-you! I always completely forget the "Alternates" section exists. You are correct, the other versions are all accounted for. 
I also forgot about the annoying background music that plays continuously on the "vs" games. Unless that's a core bug, will investigate...