I'm not sure if The Beary Family appeared on TV, but for 10 years (1962-72), Universal commissioned a series of animated shorts. I seem to recall them appearing in Gold Key comic books, in support, of course, of Woody Woodpecker, so maybe they did hit the small screen after all.
Grace Stafford (Mrs. Walter Lantz) and Paul Frees are the principal voices for much of the run, although there was a stretch where Daws Butler filled in for Frees, who was working for just about everyone in the 60's, he was in such demand.
From 1969, here's "Cool It, Charlie", in which Charlie and his son (both voiced by Frees) have issues just getting an air conditioner home.
Nothing special, really. You can picture other cartoon families having similar issues.