Is it possible she made it up? Sounds like a charming way to express affection to little you.

I found a reference to similar phrases in an article about old folk songs. I put a link below, but that particular song is not on the first page and you need to sign up to read the whole thing.

So it may well be words from a song, remembered for generations. Also, as alisande says, she could have made up the little rhyme herself.

Here is a link that might be useful: Journal of American Folklore 1947

I see now that to sign up for that site you need to be connected to an educational research group of some kind.
At any rate, further searches make me think this is from an old folk song popular in New England.

Well, it was funny. When she baked, using brown sugar, I loved for her to give me one of the little "sugar lumps" on a spoon. So she would have me say "The grass is green around the stump; you are my little sugar lump", and then she'd hold the spoon up to my mouth and I'd eat the lump.

Yes, a nice little memory. Maybe she made it up; don't know, and now she doesn't remember it .... :-(

I found it! That is a line from the second verse (which I've never heard) to the following:

Rose's Red, Violet's Blue

Nursery Rhyme
(English)

Rose's red, violet's blue.
Sugar is sweet but not like you.
The violets fade, the roses fall;
But you get sweeter, all in all.

As shore as the grass grows around the stump,
You are my darling Sugar Lump.
When the sun doesn't shine, the day is cold,
But my love for you does not get old.

The ocean's deep, the sky is blue;
Sugar is sweet, and so are you;
The ocean waves and the sky get pale,
But my love is true, and it never fails.

Oh my!!!! You certainly did find it! I'm very excited. wow - thank you so much. I've wondered for so long. My mom seems to know a poem for every occasion. She just comes out with them (yesterday she was reciting "March the sarch ...". I wonder, wonder, wonder where she first heard that line about the stump/sugar lump. It changed ever so slightly from what you found, but that's certainly it. Now I know where it comes from.

Thank you, petaloid, I'm smiling a very big smile!

Suzieque