The song is around in several versions. From Wolf Folklore Collection (post-Carter, but?); 1st part the same, but the rest is different. The "weeping willow" is absent.

IN A LITTLE VILLAGE CHURCHYARD
(My Mother's Grave)

In a little village churchyard,
There I see a grassy mound.
There my mother lies a-sleeping
In the cold and silent ground.
She was sweet and kind and tender,
But oh, those tears I cannot drive away.
Oh, I never can forget her,
For I think of her each day.

Bright the flowers bloom around her,
When the warblers sing their song.
Still I sit so sad and lonely
Since my mother's dead and gone.
I was young, but I remember
That sad day my mother died.
And I set there softly weeping
When she called me to her side.
Then she told me she was going
To where the angels sit upon the throne,
And I know we'll meet in Heaven
When life's troubled race is done.

Mrs. Alice Isringhouse, Holly Grove, AK, 1959.

http://www.lyon.edu/wolfcollection/songs/isringhousein1244.html

Just noted that they had "Baptist Monophonic and Heterophonic Hymnody in Southern Appalachia," an article readable through JSTOR which mentions the song. Is that legal? This is in reference to "Primitive Baptist Hymn Book and Tune Book," 1918, compiled by John Daily ($20-$25 at Abebooks). The article by William Talmadge is in "Anuario Interamericano de Investigacion Musical" vol. 11, 1975.


From "The Kentucky," Clark and Spelman:
"In all American music, there is no more downright melancholy than is to be found in the wailing chant of "The Village Churchyard." The ballad recites a long grief-stricken tale of a lone orphan child wringing its pale hands beside a mother's grave. The child moans:

In that dear old village churchyard,
I can see a grassy mound;
That is where my mother's sleeping,
In the cold and silent ground."

I can't tell if the authors are quoting from an old song or a 1930s cluster.