Green’s Dictionary of Slang

cogie n.

the vagina.

1761		implied in whip someone’s cogie
c.1800		‘The Reels O’Bogie’ in Bold (1979) 194: There’s Kent, and Keen, and Aberdeen, / And the town of Strathbogie, / Where every lad may have his lass / Now that I’ve got my cogie.
1890–1904		Farmer & Henley Sl. and Its Analogues.

In phrases

whip someone’s cogie (v.)

to have sexual intercourse.

1761

Nancy Dawson’s Jests 10: It was agreed, that he should whip her cogie at the end of every mile.