Yeah, the fender tag will show the scheduled build date.
I'm speculating that if Chrysler provided cars for a TV series that they would want the studios to have them ASAP to get maximum exposure of their current models. Black plates very well could have been issued because .CA hadn't switched over to the blue ones yet.
Miss Hathaway ALWAYS had brand new Dodge convertibles on the Beverly Hillbillies. The banker seemed to have Imperials.