Kirsten, not sure what you are looking for. Posted in this thread are two versions, Powder River Jack Lee from the 1930s, and Thorp's from earlier, but the basis for many later singers.
Here is the one sung by Jules Allen in the 1930s, the favorite of many of us raised at that time.

THE DYING COWBOY
Sung by Jules Verne Allen

"Oh bury me not on the lone prairie"
These words came low and mournfully,
From the pallid lips of a youth who lay
On his dying bed at the close of day.

He had wailed in pain till o'er his brow
Death's shadows fast were creeping now;
He thought of his home and his loved ones nigh
As the cowboys gathered to see him die.

O bury me not on the lone prairie
Where the wild coyotes will howl o'er me,
In a narrow grave just six by three,
O bury me not on the lone prairie.

In fancy I listen to the well known words
Of the free, wild winds and the song of the birds;
I think of home and the cottage in the bower
And the scenes I found in my childhood's hour.

It matters not, I've oft been told,
Where the body lies when the heart grows cold;
Yet grant, O grant this wish to me,
O bury me not on the lone prairie.

O then bury me not on the lone prairie,
In a narrow grave just six by three,
Where the buffalo paws o'er a prairie sea,
O bury me not on the lone prairie.

O bury me not on the lone prairie
In a narrow grave just six by three,
Where the buzzard waits and the wind blows free;
Then bury me not on the lone prairie.

O bury me not, and his voice failed there,
But we took no heed of his dying prayer;
In a narrow grave just six by three
We buried him there on the lone prairie.

Where the dew-drops glow and the butterflies rest,
And the flowers bloom o'er the prairie's crest;
Where the wild coyotes and winds sport free
On a wet saddle blanket lay a cowboy-ee.

O bury me not on the lone prairie
Where the wild coyotes will howl o'er me,
Where the rattlesnakes hiss and the crow flies free
O bury me not on the lone prairie.

O we buried him there on the lone prairie
Where the wild rose blooms and the wind blows free,
O his pale young face nevermore to see,
For we buried him there on the lone prairie.

Yes, we buried him there on the lone prairie
Where the owl all night hoots mournfully,
And the blizzard beats and the wind blows free
O'er his lowly grave on the lone prairie.

And the cowboys now as they roam the plains,
For they marked the spot where his bones were lain,
Fling a handful of roses o'er his grave,
With a prayer to Him who his soul will save.

O bury me not on the lone prairie
Where the wolves can howl and growl o'er me;
Fling a handful of roses o'er my grave,
With a prayer to Him who my soul will save.

With music, pp. 116-118, 1933 (1935) Jules Verne Allen, "Cowboy Lore," The Naylor Company, San Antonio, Texas.