The Gairdner Child - "proud Maisrie stands at her bower door, as straight as a willow wand, and syne there cam' a gardener child..." is the song that came to my mind as soon as I saw your query. I heard it on a Ewan MacColl recording. So do try to double check whether that's the tune. There is a faint resemblance to Lady Margaret (see versions in the DT) and if you have the facilities you can hear a tune for the DT Gairdner Child --the MacColl song wasn't 'a US version' however. If it's not what you want, well, happy hunting...