Definition of connies:
(n) :
A diminutive of the female given name Constance or, rarely, of Concepción.
(n) :
A diminutive of the male given names Conrad or Cornelius or, rarely, of Conway.
(n) :
(aviation, informal) The Lockheed Constellation airliner.
(n) :
Obsolete form of cony (“rabbit”). [A rabbit, especially the European rabbit, Oryctolagus cuniculus (formerly known as Lepus cuniculus).]