John built a Mansion on What is now Hilton Head Island. This article list his wife's first name as Elizabeth and that they arrived at Hilton Head in 1774. Her last name is given as Caulfield here.
He was a privateer based on Hilton Head Island during the revolution. fought for the American side.
"A Masonic Lodge was organized and a building erected between the public road and Broad Creek on the northern edge of Leamington Plantation. Captain John Stoney was Master of the Lodge for many years until his accidental death in 1821."
Hint  John Stoney, 1780-1838 (son) and his descendants.
Chronology of Hilton Head Island, A summary of memorable dates and events from 1520 to 1983 of the Common Era, by the Rev. Dr. Robert E. H. Peeples, The Heritage Library Foundation, Hilton Head Island, South Carolina. - this link broken bu a current search returned the search page for John Stoney information on the site
In Memoriam (HM5EN), Location: Hilton Head Island, SC 29928 Beaufort County, Captain John Stoney, James Stoney, John Safford Stoney. 
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It may be possible to confirm family relationships with John by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share DNA with John: