This is a tough one! The best I could do was to find out a longer title:

HARRY AND CARRIE, OR, HE SIGHED, SHE SIGHED AND THE SEA SIGHED TOO

Other facts are as you describe them.

Sheet music is held by Oxford University and by the British Library. (But you could have assumed that, right?)

(Surely this can't be the same song, but—

Allmusic.com says HARRY AND CARRIE (or HARRY AND CARRY) was recorded by Eddie Cooley & the Dimples (an early R&B group) on their album "Fever 1956-1961" (Hydra CD 27130, 2006) and "Priscilla" (Collectables CD 9937, 2005):

When Carrie saw Harry that same moonlit night,
Carrie looked into Harry's eyes and her heart just took a flight.
Yes, it's love, love, love, same old story too,
'Bout a boy meets girl to make their dreams come true.

So Harry told Carrie: "Never in my whole life
Did I ever meet such a pretty little girl that I want to be my wife."
Yes, it's love, love, love, same old story too,
'Bout a boy meets girl to make their dreams come true.)