Green’s Dictionary of Slang

a euph. for damned adj.; esp. in excls.

1925		Dos Passos Manhattan Transfer 57: Dey carried me off on a stretcher or I’m a cockeyed liar.
1926		K.S. Prichard Working Bullocks 88: Got me, y’ blasted, cock-eyed Pommy? Tell him.
1930		J. Tully Shadows of Men 199: Yes, you’re cockeyed right, I would.
1933		E. Hemingway letter 3 Apr. in Baker Sel. Letters (1981) 385: It is too cockeyed bloody hot.
1939		T. Wolfe Web and the Rock 492: You bet your cock-eyed life that’s what’s worrying me!
1946		S. Jackson An Indiscreet Guide to Soho 63: Joe Louis is my friend and he’s the champion of the whole cockeyed world.
1955		B. Appel Tough Guy [ebook] He led Joey through the Ladies’ Entrance of Quinn’s saloon [...] ‘There’s some cockeye law about minors’.
1974		R. Carter Sixteenth Round (1991) 197: Not even a cockeyed cock-a-roach could have survived there.