To suck the monkey; to suck or draw wine, or any other liquor, privately out of a cask, by means of a straw, or small tube. Monkey’s allowance; more kicks than halfpence. Who put that monkey on horseback without tying his legs? vulgar wit on a bad horseman.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Monks and Friars * MonosyllableNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes