Green’s Dictionary of Slang

1. (also jinny) a donkey [play on the songbird SE jenny-wren, i.e. a ref. to the donkey’s bray; post-18C uses are US].

a.1789		G. Parker (attrib.) ‘The Sandman’s Wedding’ in Farmer Musa Pedestris (1896) 64: Joe the sandman drove his noble team / Of raw-rumped jennies.
1843		R.S. Surtees Handley Cross (1854) 79: Three donkeys, two jacks and a jinney.
1870		B. Harte Luck of Roaring Camp (1873) 66: As they approached, they at once recognized the venerable ‘Jenny’ and the two-wheeled cart as the property of Tennessee’s Partner.
1898		J. Fox Jr ‘A Trick O’ Trade’ in Hell Fer Sartain and Other Stories n.p.: Pears like Abe had foun’ a streak o’ iron ore on the lan’, an’ had racked his jinny right down to Hazlan an’ tol’ the furriner.
1946		in Randolph & Legman Ozark Folksongs and Folklore (1992) II 639: There was never a jinny so ugly / But could get her a jackass to bray.
1970		E. Thompson Garden of Sand (1981) 17: She hee-hawed like a jenny.

2. (Scot./US, also jennie) a young woman; also attrib. [dial. jenny, a country girl].

1856		J. Strang Glasgow and Its Clubs 281: All the loose boys and elder blackguardianism of the town were attracted thither, to play tricks on what were designated the country ‘Jocks and Jennies’.
1877–78		Cornelian 86: Jenny. A female distinction [HDAS].
1917		R. Lardner ‘The Water Cure’ Gullible’s Travels 187: The mothers is all named Jennie. [Ibid.] 207: I don’t think it was the rollin’ that got me. It was one glimpse of all the Jennies and their offsprings.
1930		J. Lait Gangster Girl 47: It’s jennies like you get good men croaked.
1955		H. Braddy ‘Narcotic Argot Along the Mexican Border’ in AS XXX:2 87: JENNY BARN, n. The women’s ward in a narcotic hospital.

3. (US) menstruation.

1968

DARE III 116/1: Qu. AA27, . . A woman’s menstruation Inf NY83, I’ve got jenny.

4. the vagina.

1997		Roger’s Profanisaurus in Viz 87 Dec. n.p.: Jenny US n. Fadge; minge.
1999		Hip-Hop Connection Dec. 45: ‘Jenny’ means twat (sorry, but it does).