Here's "New River Shore." It's quite different from the Red River version, but it's easy to see that they're the same song. Note that rich R has another version of "New River shore" hidden above (click).
-Joe Offer-

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THE NEW RIVER SHORE

1 At the foot of yonders mountain
Where the tide ebbs and flows,
Where the red roses are budding
And the pleasant winds blow,

2 'Tis there I spied the girl
That I do adore
As she was a-walking
On the New River shore.

3 I stept away to her;
I says, 'Will you marry me?
'My portion is too small, sir.'
'No matter,' said he.

4 'Your beauty does please nie
And I ask nothing more.
And will you go with me
From the New River shore?'

5 So when her old father
These words came to hear
He said, 'I will deprive you
Of your dearest dear.

6 'I will send him away
Where the loud cannon roar,
And will leave you lamenting
On the New River shore.'

7 He raised for him an army
Of sixty and four
To fight her old father
On the New River shore.

8 He drew out his sword
And he waved it around
Till twenty and four
Lay dead on the ground

9 And the rest of tile number
Lay bleeding in gore,
And he gained his own true love
On the New River shore.

10 Now Pollie is married;
She lives at her ease,
She goes when she wants to,
Comes back when she pleases.

11 Now Pollie is married,
She lives in renown;
She is the grandest lady
In Baltimore town.


'New River Shore.' Reported by L. W. Anderson as collected by Delma Haywood from Mrs. Sallie Meekins of Colington, Albemarle Sound.


from the Frank C. Brown Collection of North Carolina Folklore, Volume II

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In this message (click), Jean Ritchie says she recalls hearing a song called "New River Shore" sung to something like the tune of "Slane" (Be Thou My Vision). Here's the tune from the Frank C. Brown Collection. Can't say it works for me, but I can't figure how "Slane" would work, either.

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Click to play