A Jen Too Many

I'm trying to figure out where I got this song from. I think I remember my mother singing it to us when I was a kid, but the memory is fuzzy. I started singing it to my children in the mornings when I was getting them out of bed, several years ago.

Good morning!
Good morning!
Good morning!
Good morning I say!

Good morning!
Good morning!
And have a good day!

Is anyone (siblings o' mine, chip in, please!) familiar with this song? Did my mother make it up, or did it come from some longer song?

I'll ask her, too, but honestly, I doubt she'll remember. She tends not to remember stuff like that.