I recall a cartoon that was almost certainly made before I was born. Forties or Fifties, I think. It involved a couple of anthropomorphic animals – perhaps a cat and a mouse. (I’ll use those forms unless corrected.) The cat was trying to catch the mouse, and failing every time. He finally broke down and started feeling sorry for himself. He said something along the lines of ‘I’m nothing but an old used-to-was!’ The mouse took pity on him and tried to comfort him saying, ‘Aw, you ain’t no used-to-was!’
Without doing any research, the first thought that came to mind of an animated animal character talking with a sort of southern speech pattern was Deputy Dawg. Terrytoons animated TV series from the early 60’s.
There were a number of cat-and-mouse cartoons. The ones that I’ve been able to find the names of quickly are Tom and Jerry, Punkinpuss and Mushmouse, Herman and Katnip, and Snooper and Blabber. There doesn’t seem to be any website with a list of all such cat-and-mouse cartoons.
Hm. I don’t remember it being B&W. Saturday Morning Cartoons were always in colour. I can see Porky Pig telling the dog he wasn’t a ‘used-to-was’ though. I’ll see if I can find a video tonight when I get home to a computer that has speakers.