Hi,
Don't know if you've seen
The Stewarts of Ballintoy : with notices of other families of the district in the seventeenth century from Google Books. A quick copy & paste gives a bit of info on the family. Evidently there was at least one daughter from William & Rose's marriage whose married name became Hill. Their son, William Hill, lived at Moiyarget.
Page 14:
The man named William Fullerton, who assisted in 1641 to hold the Castle of Ballintoy against the insurgent Irish, is reported to have left a large family. Several of his descendants in the eighteenth century were well known. One of them, also named William Fullerton, married Rose Montgomery, of Moiyarget, and the late William Hill of the same place was their grandson. Another brother, named David Fullerton was a Presbyterian minister of Carrickfergus, from 1750 to 1766, and died the rector of a parish near Kingston, Jamaica, in 1789. A third, named George Fullerton, emigrated to Virginia, in America, and was slain fighting on the side of the Colonists, in the war of Independence. He left one daughter, Catherine, who became sole heir to her uncle, Alexander Fullarton. The latter had been educated as a doctor, and accumulated a large amount of wealth in Jamaica. On his return, he purchased the Ballintoy estate for the sum I £20,000 and having no family, although married, he bequeathed this fine property to his niece, as already stated, whose son, according to his will, was required to take the name of Fullerton. This lady married Dawson Downing, Esq., of Ballaghy and Rowesgift, in the county of Derry. She left one son, George Alexander Fullerton, who was born in the Mansion, Ballycastle, November, 1775, and died at Toekington Manor, Gloucester, in 1847. He left three sons and five daughters. His eldest son and heir named Alexander George, wa born in 1808, and married in 1853 the Lady Georgiana Leveson Gower, second daughter of the late Earl of Granville. Their son, William Granville Fullerton, was born at the British Embassy, Paris, in 1834, and died just when he had attained his majority, in 1855. The Ballintoy estate is still owned by a representative of the family.
http://archive.org/stream/stewartsofballin00hill#page/n35/mode/2up/search/Jamaicabrigau
*edit to add from thje same source:
The first Alexander Montgomery, above mentioned, lived and died in Moyarget, leaving one daughter, Rose, who married William Fullerton. Their daughter, Mary Fullerton, married Adam Hill, of Moyarget, and their son, William Hill, of the same place, died in I854, at the age of eighty years. The writer of this account was a son of William Hill.
