In the episode “Scratch My Car and Die!”, Rob buys a new sports car called the “Tarantula” (according to Buddy, its nickname is the “T-Bug”). Since the episode aired in early 1964, we can assume the car is the '64 model.
Since the car is of course fictional, we never see it during the episode. But the characters make several comments regarding its appearance. It is low and sleek (so aerodynamic that its ash trays are teardrop-shaped); its trim is not chrome, but stainless steel; it has bucket seats, front fins and rear wings; and, in lieu of a trunk, it even has an auxiliary motor!
It’s not explicitly stated that the car is a convertible, but that seems likely in view of Rob’s purchase of a British driving cap (which also may be a clue to the car’s country of manufacture).
Combining all these facts, I envision the car as being sort of a cross between an Austin-Healy 3000 and a Lincoln Futura. So, here is my speculative illustration of the 1964 Tarantula. I have assumed that Rob would pick the British Racing Green finish.