The Confederation of Galactic Limmie was a Limmie league that existed from the years 47 BBY to 30 BBY, when it folded due to financial troubles. Major franchises included the Coruscant Senators, who led the exodus of teams out of the league when it hit financial troubles.
Talks occurred in 234 ABY to potentially bring back the Confederation as a lower-level pro Limmie league, but nothing of substance ever came out of it. It is widely assumed that no league with the name will ever exist again.