In Australia this appeared on 'The Atom Ant Show' along with Precious Pupp - though I gather it appeared on about 4 other US shows.
Hillbilly Bears was produced in 1965, which I consider something of a turning point for Hanna Barbera. Roughly speaking, nearly everything they'd made up until this point was at least half reasonable. After around this time though, they began their long downward spiral which would last 20 years, and precious little of any worth came out of the studio (or TV animation in general) from the late 60's to the mid 80's.
Perhaps a little surprising then that Hillbilly Bears isn't that awful. Firstly, it was produced during their 1958-65, initial 'good' period. Then consider that the writers were Chuck Jones' partner Michael Maltese (What's Opera Doc?, Duck Amuck) who started moonlighting for some of HB's better shows towards the end of Warner's existence. Then consider he brought with him another golden age WB writer, Warren Foster, and remember it wasn't all that long since Hanna and Barbera had been directing Tom and Jerry, and maybe it doesn't seem that surprising.
The Hillbilly Bears were a family of sterotypical...err... Arkansans? They were pleasantly dumb in a Ma and Pa Kettle sort of way. The plots never amounted to anything much. Paw was generally fuedin' with the neighbours, or anybody else who happened along. The most memorable feature, by a mile, was Paw Rugg's trademark, wheezy chuckle. Most of his other dialogue was pretty much mumbled and indecipherable, with the odd word being semi-legible (he reminds me somewhat of my Uncle Ken).
The set piece of the character with no lines, but a trademark vocal mannerism was carried over even more memorably in Precious Pupp's infectious trademark snigger, voiced by Don Messick, changed slightly and less appealingly for Mutley a few years later.
The way things are going, this will be out on DVD one of these days, along with Secret Squirrel, Squiddly Diddly, Atom Ant, Winsome Witch, and Precious Pupp. I can't hate it too much. It was from the days when Hanna Barbera still had a bit of a clue. Plus, it was syndicated on TV when I was a kid. Perhaps I'm seeing it through slightly rose-fogged glasses.