This was a short lived series that ran from 1983-1986.
The original car was a modified Manta Montage Kit Car on VW chassis
The production Manta Montage used a VW chassis with the side pans cut
out out and the Montage body fit over the
remaining backbone. The Montage was modified for the show by removing
the bubbleback rear window and replacing it with a
flying buttress, like the 68-77 Corvettes. The car may have used a
Porsche or Corvair engine and transaxle, but I can't confirm
this.
There was also a second Coyote version used later in the series. It
was built on a Delorean backbone mated to a pantera zf
tranny with built V6. The change was due to Brian Keith's inability
to get in and out of the first car with ease. This car was seen
in poor shape last year at MGM Studios, Florida.