Green’s Dictionary of Slang

(US black) the penis.

1929		in Randolph & Legman Ozark Folksongs and Folklore (1992) I 502: ‘He pulled out his big long sting-a-ma-ree, / He says, Ain’t that a beauty!’ [...] Sung [...] by Mr. L.R., Poplar Buff, Missouri, September 13, 1929. He heard it in 1898.
1956		N. Algren Walk on the Wild Side 79: Daddy I don’t want your money / I just want your stingaree.
1993		Charlie Musselwhite [song title] Stingaree.