Lyrics transcribed from the sheet music images at The Lester S. Levy Collection of Sheet Music. (These lyrics are only slightly different from the ones posted by Kendall above.)

WILL YOU LOVE ME WHEN I'M OLD?
(J. Ford, 1872)

I would ask of you, my darling, a question soft and low
That gives me many a heartache as the moments come and go.
Your love, I know, is truthful, but the truest love grows cold.
It is this that I would ask you: will you love me when I'm old? (2x)

CHORUS: Life's morn will soon be waning and its ev'ning bells be toll'd,
But my heart will know no sadness if you'll love me when I'm old.

Down the stream of time together we are sailing side by side,
Hoping some bright day to anchor safe beyond the surging tide.
Today our sky is cloudless, but the night may clouds unfold,
And its storms may gather 'round us. Will you love me when I'm old? (2x)
CHORUS

When my hair shall shame the snowdrift and mine eyes shall dimmer grow,
I would lean upon some loved one in the valley as I go.
I would claim of you a promise worth to me a world of gold.
It is only this, my darling: that you'll love me when I'm old. (2x)
CHORUS

[A text only slightly different from the one above was "collected" by John Quincy Wolf, Jr. in Pleasant Grove, Arkansas in 1952. Click here. (An mp3 file is allegedly available, but it didn't work for me.)

That page says that Vance Randolph also collected it.