Green’s Dictionary of Slang

1. to trifle with, to fool around.

1889

189019001910192019301940

1949

1889–90		Barrère & Leland Dict. of Sl., Jargon and Cant.
1920		R. Lardner Big Town 164: The Mrs. told Kate she was a hick to be monking round with a jockey.
1949		J.H. Burns Lucifer with a Book 180: He looked from his windows at the moonlight monking it up with the breast of the nunlike snow on the meadows.

2. to neck, to engage in sexual activity.

1975

196019651970

1960

1960, 1975

Wentworth & Flexner DAS 343/1: monk [...] To neck. Some c1935 student use; never common.