Green’s Dictionary of Slang

1. a Constellation airliner.

1953

R. Chandler Long Good-Bye 28: Nobody from L.A. wants to ride a DC-3 over mountains when he can take a Connie and make it in seven hours to Mexico City.

2. a Lincoln Continental.

1972		G.V. Higgins Friends of Eddie Coyle 84: They're the owners of record for about nine Lincoln Connies and at least four Cads.
1978		S. King Stand (1990) 151: The Connie blazed on up the road.
2004		Muscle Car Collection 🌐 So, he ditches the corpus-delicti, assumes the guy’s identity, and gets behind the wheel of the Connie [i.e. a 1941 V-12 Lincoln Continental convertible].