Very close, Mick: it was in vol.VIII no.1 (1956), and was recorded by Peter Kennedy and Sean O'Boyle from Charles O'Boyle of Belfast (Sean's father), 7th July 1952. The final half-verse was sung to the first half of the tune, with the final phrase marked rallentando. Tune and text differ in places from your (admirable) recollection, so I'll quote it as originally noted (except for the spelling of brown as broun):

LADY MARGARET (SWEET WILLIAM'S GHOST)

(Recorded by Peter Kennedy and Sean O'Boyle from Charles O'Boyle of Belfast , 7th July 1952)

Lady Margaret sat in her bow window, sewing her silken seam,
When a grievous ghost chanced to pass by, most wonderful to be seen.
"Are you my father Phillip?", she said, "Are you my brother John?
Or are you my true-love Willy, to fair Scotland has come home?"

"I'm not your father Phillip", he said, "nor yet your brother John,
But I'm your true-love Willy, to Scotland has come home."
"Did you bring me the gold, dear Willy, did you bring me the lace?
Did you bring me the bonny brown dress, my fair body to embrace?"

"I brought no gold, dear Margaret", he said, "and I forgot the lace,
But now I carry my winding sheet through many's the dreary place.
The cock crew once, dear Margaret", he said, "'tis wearing nearer the day.
Come give to me my faith and troth that I once gave to thee".

"Your faith and troth, dear Willie", she said, "you ne'er will get from me
Till you come down to yon bower and give me kisses three".
"The cock crew twice, dear Margaret", he said, "'tis wearing nearer day.
Come give to me my faith and troth that I once gave to thee".

"My nose is ate with the worms, dear Margaret, my breath it is mighty strong
And if I would kiss you bonny fair lips your days would not be long.
The cock crew thrice, dear Margaret", he said, "'tis wearing nearer day.
Come give to me my faith and troth that I once gave to thee".

She tilted up her bonny brown dress a-far above her knee,
For the lee long length of the dark winter's night the dread corpse followed she
Until she came to Saint Bernard's churchyard and sat down on a stone
When she saw the grave a-opening to let her Willy in.

She lifted up her bonny white hand and stroke him on the breast, breast.
Saying, "There's your faith and troth, dear Willy, I hope your soul's at rest!"

Child #77   Roud no. 50

Journal of the English Folk Dance and Song Society, vol.VIII no.1, 1956.

"Charles O'Boyle: Age 74 at the time of recording; died shortly afterwards. Father of Sean O'Boyle who worked as a collector for the BBC in Northern Ireland. Charles inherited much of his own singing tradition from his mother, who was born in Donaghadee, Co. Down, where there is a strong Scots tradition, but she lived most of her life in Belfast. He was a teacher, but from 1914-20 (interrupted by the war) studied and worked in Cork with Hardebeck. He became secretary to Hardebeck, who was blind, and made musical and Gaelic transcriptions and translations for him. His work is acknowledged by Hardebeck in the preface to Pt. III of Gems of Melody. (Pigott)." - Peter Kennedy.

A.L. Lloyd commented, "The tune is an interesting Mi pentatonic variant of the ubiquitous Dives and Lazarus tune".

To complement Mick's abc, here is a (slightly different) midi made from the notation in JEFDSS, as transcribed by Peter Kennedy and Michael Bell from the recording of Charles O'Boyle's singing:

Sweet William's Ghost (midi).

As to Michaelr's question, Newfoundland wasn't settled solely from Ireland (!) and a lot of English and Scottish traditions persist there too, though perhaps less obviously. In this case, the earliest known examples of the song are Scottish; it spread to Ireland, and has been found quite widely there in the North; some of the tunes to which versions are sung are certainly Irish in origin (though not, of course, The Star of the County Down / Dives and Lazarus / Gilderoy). It wouldn't be surprising if the bulk of examples from Newfoundland had got there via Ireland.