The song is The Broken-Hearted Lover [Real Audio] by the Carter Family.

THE BROKEN HEARTED LOVER

Would you let her part us, darling
Could you truly turn away?
Would it make your heart ache, darling
Not to see me night or day?

I've been dreaming of you, darling
Dreaming of your eyes so blue
Take me back, for love I'm dying
For I love none else but you

[INSTRUMENTAL BREAK]

Many a day with you I've rambled
Down by the shades of the deep blue sea
There you told me that you loved me
That you loved none else but me

I've been dreaming of you, darling
Dreaming of your eyes so blue
Take me back, for love I'm dying
For I love none else but you

[INSTRUMENTAL BREAK]

I will give you back your letter
And your picture I love so well
How it makes my heart ache, darling
Oh, 'tis hard to say farewell

I've been dreaming of you, darling
Dreaming of your eyes so blue
Take me back, for love I'm dying
For I love none else but you

~Masato