At long last, I've received a copy of the actual published sheet music to I'll Twine 'Mid the Ringlets. It pretty much matches what Genie wrote above in 2001. Here are the actual lyrics, verbatim (including original italics, punctuation, and capitalization):

I'll twine 'mid the ringlets
Of my raven black hair,
The lilies so pale
And the roses so fair,
The myrtle so bright
With an emerald hue,
And the pale aronatus
With eyes of bright blue.

I'll sing, and I'll dance,
My laugh shall be gay,
I'll cease this wild weeping
Drive sorrow away,
Tho' my heart is now breaking,
He never shall know,
That his name made me tremble
And my pale cheeks to glow.

I'll think of him never
I'll be wildly gay,
I'll charm ev'ry heart
And the crowd I will sway,
I'll live yet to see him
Regret the dark hour
When he won, then neglected,
The frail wildwood flower.

He told me he loved me,
And promis'd to love,
Through ill and misfortune,
All others above,
Another has won him,
Ah! misery to tell;
He left me in silence
No word of farewell!

He taught me to love him,
He call'd me his flower
That blossom'd for him
All the brighter each hour;
But I woke from my dreaming,
My idol was clay;
My visions of love
Have all faded away.

- Taken from published sheet music in the Department of Special Collections, Stanford University Libraries: I'll Twine 'Mid the Ringlets. Words by Maud Irving. Music by J.P. Webster. Copyrighted and Published (1860, 1862) by H.M. Higgins, 117 Randolph Street, Chicago. Pearson, engraver. (The "1860, 1862" signifies that this is from an 1862 compilation published by H.M. Higgins entitled "WESTERN GEMS: SONGS COMPOSED BY J.P. WEBSTER." The page showing I'll Twine 'Mid the Ringlets shows the 1860 date.) I'd post a scan online but Stanford requires permission for further reproduction.