Was this something like 'the last of its kind?'
I can remember this show rather dimly from when I was a kid, and I'm not sure why we didn't watch it more regularly [and by "we" I mean the whole 2-parent, 4-kid family with our only TV]. But I do remember the main character was always called "Nanny," as if that were her name, and that she had some kind of magical and/or telepathatic powers. But, unlike "Bewitched" or "Jeanie," she did not seem to have a 'normal' person who knew all about her and her powers and she was not overt, per se, in the things she did [I mean she didn't bring historical characters to life in the present, or teleport herself anywhere in the world, and such things]. It was always more subtle, like getting circumstances to come together for the family's benefit, or planting the right idea in their minds. I don't remember what some posts talk about here, that she did give hints of her extraordinary abilities by saying who was at the door or saying she will get phone just before it even rings; but that may just be because of the few episodes I saw, let alone remember.
So what I mean by "last of its kind" is a sitcom with the character of supernatural abilities living among 'normal' people with much potential for both creating and solving complications. Furthermore, the setting is in the era of television of much greater propriety-- essentially before All in the Family completely changed the foci of sitcoms. Nanny is in some ways like Samantha, Jeannie, or Uncle Martin, but just more temperate in using those special abilities. And as far as I recall, she put herself into per position by simply wanting to be there, with no ultimate ambition to be somewhere else or relatives who try to pull her away or sabotage her benevolence.
Anyway, I tend to think this show, should I be able to see it again, I might think is the one that got the idea right. The others I mentioned were just too far out most of the time.