Green’s Dictionary of Slang

Conny n.

(US teen) nickname of the Conti Cardigan (created by an eponymous Greek clothier) and one of the preferred garments of members of sharpie n.2 gangs c. 1970.

[Aus](con. 1960s-70s) T. Taylor Top Fellas 45/2: Originally sharps bought their Connys off the shelf, but pretty soon kids started brigning i their own designs, sparing no expense to wow their mates.