I don't know about a black '67 Yenko but there was 1 black '68 Z/28 Convertible made.
Here's the story about it.
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This Z may be the rarest Camaro of all - There was only one 1968 Z/28 Camaro Convertible ever built, which was built for Chevrolet General Manager Pete Estes on July 15, 1968. Options included a folding rear seat, auxiliary console-mounted instruments, auxiliary lighting, power windows, remote outside mirror, custom seat belts, performance suspension package, four-wheel disc brakes, blue light stereo system, posi-traction, ë69 prototype fiberglass hood, cross-ram air and powder coated factory headers. This car was then delivered to Mr. Estes through Bill Markley Chevrolet in Detroit. The Z was used as Mr. Estes daily transportation until December 17, 1968. On that day, it was officially sold to its first owner, T.H. Standen. Mr. Standen sold the car to Vern Nye, another GM employee, only two years later, in whose hands it remained for nearly 20 years. Only recently was the car made known to the public. The car was sold at auction to the Rock 'n Roll Toy Store, LTD., in Highland park, IL. So how did this "only Z" come to be built at all? According to Jim Mattison, who worked in the special projects division at the time, they needed approval to build the Z/28 for the general public instead of trying to build just enough to homologate for SCCA racing. They figured that if Pete Estes, the Chevrolet General manager, drove a Z/28 he would like it enough to approve the plan. The problem was that Estes was a convertible freak, and he wouldn't drive anything else. They could give him a regular Z/28 coupe but it would probably just sit in the company garage. They decided the only solution was to build a convertible Z/28 and give that to Estes. The result - Estes drove the car, loved it, and we got the Z/28.
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'68 Z/28 Convertible