1966 Barracuda Vinyl Top

Vinyl top option was available on 65 and 66 Barracudas. Check your fender tag under letter "V" for the color your car came from the factory with. Number "7" under the "V" indicates a white vinyl top while the number "6" indicates a black top.
The vinyl top on my 66 Barracuda was replaced by a local upholstery shop using readily available and mostly correct looking material. A good shop should have no problem replacing it.
The vinyl option does require special moldings for the drip edge, lower front post and across the roof above the rear window line. If these parts were not included when you purchased your car, you may luck out and get a set from someone who elected to delete the vinyl top.
My guess is your car originally came with a light yellow or cream paint and black vinyl top. Nice looking combo.
Here is a picture of my car. Good luck.

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Everything you have said matches up with my build sheet..Bright Yellow, Black Vinyl top. That's what I'm going for, It also came with A/C, but I don't have ANY of that except the heater box, so the A/C will have to wait (maybe forever). Do you know anything about the windshield gasket possibly being different than non-vinyl top gaskets?