I Never Loved But One is "Those Dark Eyes" by Armand in 1865. It's been recorded as "Dark Eyes" and probably was titled differently by the Carters in 1932 to avoid copyright issues.

Her's the sheet music:

http://memory.loc.gov/cgi-bin/query/D?dukesm:1:./temp/~ammem_0URU::@@@mdb=mcc,gottscho,detr,nfor,wpa,aap,cwar,bbpix,cowellbib,ca

I NEVER LOVED BUT ONE- Carter family

                   Onward to the eastern skies,
                   With mooing efforts kissed the sea
                   I sigh and think of those blue eyes
                   That have hope and love for me

                   For they, o they have stole away
                   The heart that truly once was mine
                   Like some lone bird without a mate
                   My weary heart is desolate

                         I look around but cannot trace
                         One welcome word or smiling face
                         In gazing crowds I am alone,
                         Because I never loved but one

                         [INSTRUMENTAL BREAK]

                   Come up closer to me now,
                   Your chestnut hair is touched with snow
                   But still it is the same dear face,
                   I loved so well long years ago

                   The same as on that winter night,
                   You bent to me and kissed my brow
                   Happy hours of trusting love,
                   Oh well, they're all over now
                  
                   And I must sail the whitening foam,
                   Till I can see a foreign home
                   Till I forget that fair sweet face,
                   I ne'er can find a resting place

                         I look around but cannot trace
                         One welcome word or smiling face
                         In gazing crowds I am alone
                         Because I never loved but one