Green’s Dictionary of Slang

1. an absurd situation, a ‘nonsense’.

1969

Harper’s Mag. Aug. 100: The most asinine and inept piece of cockamamie that I’d seen all year.

2. (also cockamamee) an absurd, eccentric person.

1935		S. Kingsley Dead End Act III: Haf an hour wid at cockamamee yuh’d be dead!
1944		A. Kapelner Lonely Boy Blues (1965) 8: A terrible curse on that cockamamee, Emily Post and her goddam Bible on Formal Introductions.
1950		A. Laurie Bird Cage 18: Who started this cockamamie, anyway? [...] I know you didn't make it up out of whole cloth. Where'd you get it?