See old thread LYR/MUS ADD: Mary of Argyle, which includes the melody in abc format, though it neglects to credit the writers of the song and suggests, quite wrongly, that there was some unnamed 'American lady' involved.

Undated sheet music published in America can be seen at The Lester Levy Sheet Music Collection:

Mary of Argyle. A Favorite Scotch Song for the Piano-forte or Guitar

Words by Charles Jefferies, music by Sidney Nelson, c.1855. They also wrote 'The Rose of Allendale' and other successful songs of the era but, to the chagrin of some compilers of popular Scottish Song anthologies, they weren't Scottish.