Black Tillie
Black Tillie was Uncle Jesse's moonshine running car. When it first appeared in High Octane, the car was simply known as Tillie. The adjective "sweet" appears in the closed captions with a lowercase "S", so the car's name was never "Sweet Tillie". When they unveil the car, the Balladeer describes it as "A real sweetheart with a leaded body, a hard engine, and racing shocks." He goes on to say, "Though he hadn't made a run with her in several years, old Jesse kept her tuned up and ready.
The car used in High Octane was a 1971 Ford Custom 500, the same model as the car driven by Burt Reynolds in the 1973 movie White Lightning. The car was a dull black color, and had had all of its chrome either removed or painted over.
It's not clear what became of the Ford Custom 500, but when Jesse needed a car to race Boss Hogg in the season 2 opener Days of Shine and Roses, he borrowed a tatty 1967 Ford Mustang from Cooter. This time he named the car "Black Tillie II". Given that the episode started with old movies showing Jesse driving a 1940s car which he referred to as "Black Tillie", the Mustang should have been at least "Black Tillie III".
The only other time that Black Tillie gets a mention is near the start of Dukes Meet Cale Yarborough.