Green’s Dictionary of Slang

unfair, crooked (esp. by pre-arrangement).

1830		Ely’s Hawk & Buzzard (NY) 3 July 2/1: I saw one of Crazy John’s barney printers setting up a song with my name [...] as its author. This is done no doubt to decive [sic] the Public.
1897		Mirror of Life 20 Jan. 3/2: Mace and Donovan showing how battles were lost and won in the ‘brave days of old’ reminds us how barney fights were often made.
1903		A. Binstead Pitcher in Paradise 128: Those two getabits [...] will get up a dud or barney fight right under your nose.