Green’s Dictionary of Slang

(US) an intensifier implying a very small amount; usu. constr. with not a.

1926		Alberta Hunter ‘I Got a Mind to Ramble’ 🎵 Folks, I ain’t got a crying penny, my poor feet are on the ground.
1929		A.T. Rogers ‘Casual Observer’ in Charlotte Obs. (NC) 10 Feb. n.p./6: ‘Run up a check for eighty nine slugs an en tryna tell me yez ain’t got a cryin’ deemer between yez’.
1947		N. Algren ‘Single Exit’ in Entrapment (2009) 81: I ain’t cost you a cryin’ dime.