In the sixth episode, "Runaway Kid," Barney owns a car.
At the end of the episode Myrt tries to talk Barney out of arresting her and says he can have a sweet 1958 car that's been up on blocks since 1959!
[Barney & Andy are on the porch waiting to see the car Barney might buy]
Barney: This is just about the biggest thing I ever bought.
Andy: It's a major step.
Barney: Last big buy I made was my Mom's and Dad's anniversary present.
Andy: What'd ya get 'em?
Barney: Septic tank.
Andy: [amazed] For their anniversary?
Barney: Yeah. Oh, they're really hard to buy for. Besides, it was something they could use. They were really thrilled... 2 tons of concrete, all steel-reinforced.
Andy: You're a fine son, Barn.
Barney: Well, I try.
Ellen Corby who plays Myrt went on to play the role of Grandma in The Waltons.