Green’s Dictionary of Slang

(N.Z./US) the penis.

1994		Calt I’d Rather Be the Devil 236: [H]is ailment [. . .] involved a tumorous growth on his penis. As James put it, the malefactor was trying to ‘kill my coozie’.
2003		McGill Reed Dict. of N.Z. Sl. 51: coozer The penis, the active object aimed at the cooze, the vagina.