Green’s Dictionary of Slang

1. a prostitute; thus cony-catching, prostitution.

1593		Nashe Christ’s Teares in Works IV (1883–4) 143: It is a hundred parts more hatefull than Conny-catching: it is the Nurse of sinnes, without the which, the fire of them all would be extinguished.
1607		Dekker & Webster Northward Hoe V i: Your wife is a Tilt-boate, any man or woman may goe in her for money ; she’s a Cunny-catcher.

2. a prostitute’s customer.

1624		Massinger Renegado IV i: All is come out, sir. We are smok’d for being cunnicatchers, my master is put in prison, his she customer is under guard.
1626		Jonson Staple of News IV i: mirth.: I wonder they would suffer it; a foolish old fornicating father to ravish away his son’s mistress. [...] tat.: Marry, I would have the old coney-catcher cozen’d of all he has.
1772		Bridges Burlesque Homer (3rd edn) 23: The old coney-catcher spoke.

3. the penis.

1680		M. Stevenson Wits Paraphras’d 29: So well you tickled up my Toby, / I never cou’d endure this Looby. / Full well my Father knows, the Letcher, / What ’tis to love old Cony-catcher.
1890–1904		Farmer & Henley Sl. and Its Analogues.