I believe that the show that I would like help identifying was a summer fill in. I also think that it might have aired for two short seasons. I was quite young when it was on so I will guess that it was on some time between 1982 and 1987.
Other than where I was when I saw it which is of no use to anyone trying to identify it, literally the only thing that I remember about this show was that it was about a pair of mismatched roommates: a young black woman and an elderly white woman. They of course had different world views.
It rang no bells, but googling sitcom with a young black woman and an elderly white woman turned up Me and Mrs. C., which ran in the summers of 1986 and 1987. Here are its opening credits and IMDb page. Enjoy!