Green’s Dictionary of Slang

conycatch v.

also cony, cunnycatch
[cony n. (3)/cony n. (2a)]

1. [late 16C–17C; early 19C] to ensnare in a confidence tric; thus conycatching, swindling, cheating.

2. [17C] to go out whoring or womanizing; thus cony-catching n., whoring.