Well, I've done some more treaking of the tune, primarily in resolving the melody after the final verse with an extra line (copy and Paste into WORD/TIMES/11 to line up the chords):

From SONGS AND CHANTIES 1914-1916, by Cicely Fox Smith, Elkin Mathews, © 1919, pp. 86-88
Adapted for singing by Charles Ipcar, © 2005
Tune: adapted from 19th century gospel song "Little Black Train"
Key: F (5/C)
RIO GRANDE


F-C-----------F---C----------------C'-------------C
A ship lies at her moorings, out there in the stream;
---F----------------------------------------------F'
Her lines upon the water are lovely like a dream,
C'--C--------------F------C--------------C'---------------C
And like a dream she'll slip away in the dawn-ing gleam,
-----------F------------------------------------C
For she's bound for Ri-o Grande in the morning;
-----F-----C--------------F--C---------------------------C'------------C
Yes, she's bound for Ri-o Grande, and it's there that I would be,
----F-----------------------------------------------F'
And every rope aboard her is singing to be free:
C'-C-------------F----C---------------------------C'-------------C
It's good-bye to your sweetheart dear, good-bye to your bride,
-----------F---------------------------------------------------F'
For she's bound for Ri-o Grande, with the morning tide!

Chorus:
C'---C--------------F-C---------------------------C'-----------------C
She's bound for Ri-o Grande, and it's there that you would be,
-----F-----------------------------------------------F'
And every rope aboard her is singing to be free:
C'-C-------------F-----C---------------------------C'------------C
It's good-bye to your sweetheart dear, good-bye to your bride,
-----------F---------------------------------------------------F'
For she's bound for Ri-o Grande, with the morning tide!


Now I heard the seagulls piping, and all they seemed to say
Was, "Rise up, young sailorman, it's time to sail away;
Oh, heave your donkey's breakfast in, you can no longer stay,
For you're bound for Rio Grande in the morning;
Yes, you're bound for Rio Grande, and oceans two or three,
And ports a plenty up and down for lively lads to see,
Across the seven seas, Johnnie, round the world so wide,
For you're bound for Rio Grande, with the morning tide!" (CHO)

The lights in Paddy Ryan's bar, still shining on the shore;
Bid your pals good-bye, Johnnie, it's time to pay your score;
You don't want to see or smell this harbour any more,
For you're bound for Rio Grande in the morning;
And it's "Away My Rolling River" – as the sun puts out the stars –
A-tangle in her royal yards, with the frost still on her spars;
The deep sea hunger's got her, and it's not to be denied,
For she's bound for Rio Grande, with the morning tide! (CHO)
Final:

C'---------C------------------G--------C-----F
Yes, she's bound for Ri-o Grande in the morning;

I'm not sure if this is original or not but a C' means to me that I'm chording a higher C on the next, or at least picking the melody note higher.

Cheerily,
Charley Noble