The rhyme is almost identical to Little Betty Winkle, She Had a Pig...
Billy Pringle had a little pig,
When it was young it was not very big,
When it was old it lived in clover,
Now it's dead and that's all over.
Billy Pringle he lay down and died,
Betty Pringle she lay down and cried,
So there was an end of one, two, and three,
Billy Pringle he, Betty Pringle she, and the piggy wiggy* wee.
*"Wiggy" can mean "wearing a wig". When "piggy" is next to "wiggy", as in "piggy wiggy", it's a kids way to rhyme with "piggy". It can mean "little piggy" or it can playfully refer to the child. In this rhyme, it means "little piggy".
Here's another version of this rhyme from Traditional Nursery Songs of England with Pictures by Eminent Modern Artists edited by Felix Summerly (1843):
Did You Not Hear of Betty Pringle's Pig!
Did you not hear of Betty Pringle's pig!
It was not very little nor yet very big;
The pig sat down upon a dunghill,
And there poor piggy he made his will.
Betty Pringle came to see this pretty pig,
That was not very little nor yet very big;
This little piggy it lay down and died,
And Betty Pringle sat down and cried.
Then Johnny Pringle buried this very pretty pig,
That was not very little nor yet very big,
So here's an end of the song of all three,
Johnny Pringle, Betty Pringle, and little Piggy.
Thanks and Acknowledgements
The illustration and the 1st version of the rhyme are from The Baby's Bouquet, A Fresh Bunch of Rhymes and Tunes by Walter Crane (1878).