The Library of Congress American Memory Collection has these:

BINGEN ON THE RHINE
Words by the Hon. Mrs. Norton. Music by H. S. Saroni.
"As sung by Miss Julia Northall"
Published by G. P. Reed, Boston, 1847.

BINGEN ON THE RHINE
Words by Mrs. Norton. Music by Chas. L. Ward.
"As sung by S. C. Campbell"
Published by D. P. Faulds, Louisville, Kentucky, 1865.

BINGEN ON THE RHINE; OR, A SOLDIER OF THE LEGION
Words by the Hon. Mrs. Norton. Music by Judson I. Hutchinson.
"Sung by John W. Hutchinson at the concerts of the Hutchinson Family"
Published by S. Brainard's Sons, Cleveland, 1883.
[The Lester S. Levy Collection of Sheet Music has an older copy, published in 1850.]

RICHMOND ON THE JAMES and BINGEN ON THE RHINE
This contains the text of BINGEN ON THE RHINE, by The Hon. Mrs. Norton, plus the following lyrics:

RICHMOND ON THE JAMES
Words by "Exile." Music by J. E. Bayley.
Published by Blackmar & Bro., Augusta, Georgia, 1864.

1. A soldier boy from Bourbon lay gasping on the field
When battle's shock was over and the foe was forced to yield.
He fell, a youthful hero, before the foeman's aims
On a bloodied field near Richmond, near Richmond on the James.

2. But one still stood beside him, his comrade on the fray.
They had been friends together through boyhood's happy day;
And side by side had struggled on field of blood and flames
To part that eve near Richmond, near Richmond on the James.

3. He said, "I charge thee, comrade, the friend in days of yore,
Of the far, far distant dear ones that I shall see no more,
Though scarce my lips can whisper their dear and well-known names,
To bear to them my blessing from Richmond on the James.

4. "Bear my good sword to my brother, and the badge upon my breast
To the young and gentle sister that I used to love the best;
But one lock from my forehead give the mother still that dreams
Of her soldier boy near Richmond—near Richmond on the James.

5. "Oh, I wish that Mother's arms were folded round me now,
That her gentle hand could linger one moment on my brow;
But I know that she is praying where our blessed hearth-light gleams
For her soldier's safe return from Richmond on the James.

6. "And on my heart, dear comrade, close lay those nut-brown braids
Of one that was the fairest of all our village maids.
We were to have been wedded, but death the bridegroom claims,
And she is far, that loves me, from Richmond on the James.

7. "Oh, does the pale face haunt her, dear friend that looks on thee?
Or is she laughing, singing in careless girlish glee?
It may be she is joyous, and loves but joyous themes,
Nor dreams her love lies bleeding near Richmond on the James.

8. "And though I know, dear comrade, thou'lt miss me for awhile,
When their faces—all that loved thee—again on thee shall smile,
Again thou'lt be the foremost in all their youthful games,
But I shall lie near Richmond—near Richmond on the James."

9. And far from all that loved him, that youthful soldier sleeps,
Unknown among the thousands of those his country weeps;
But no higher heart nor braver, than his, at sunset's beams,
Was laid that eve near Richmond—near Richmond on the James.

10. The land is filled with mourning, from hall and cot left lone.
We miss the well-known faces that used to greet our own;
And long poor wives and mothers shall weep, and titled dames,
To hear the name of Richmond—of Richmond on the James.