Green’s Dictionary of Slang

(US) the penis.

1941		(con. 1900s) in Randolph & Legman Ozark Folksongs and Folklore (1992) II 763: Cheat your partner, swing Miss Lucy, / Up with her petticoat, out with your ducey.
1953		Randolph & Wilson Down in the Holler 100–1: Ducey, pronounced to rhyme with Lucy, is a very common word for penis.
1992		Randolph & Legman Ozark Folksongs and Folklore I 395: Grease my ducey, not the deuce (two) at cards, but doosey or doozy, here for penis, usually a slang superlative or approbative, on the carefully correct pronounciation of the name of the great Italian actress, Eleonora Duse, who ‘knocked ’em in the aisles’ with her intense dramatics at her American début in 1893.