Coghill is the son of John Coghill of Knaresborough, North Yorkshire, judge of the prerogative court and one of the masters in chancery. His mother is the daughter of Tobias Cramer, of Ballyfoyle, County Kilkenny. Two elder sisters and a younger brother, James, survive infancy. He spends his childhood in Dublin.
Coghill occupies a prominent place in the life of Dublin, and is remarkable for his early display of ability. At the age of fourteen he enters the University of Dublin, graduating at the age of eighteen as a Bachelor of Laws. At the age of nineteen he is returned to Parliament and at the age of 26 he becomes judge of the prerogative court.
In Parliament, from 1692 to 1713 Coghill is a representative of the borough of Armagh, and from 1713 until his death in 1739, a representative of the University of Dublin. He is politically close to William Conolly, speaker of the Irish House of Commons, who dies in 1729. Upon Conolly’s death he succeeds him as a commissioner of the revenue. Over the following years he plays a prominent role in parliament, particularly on financial matters. He also builds up a close relationship with John Perceval, the British Prime Minister‘s chief advisor on Irish affairs.
Coghill becomes Chancellor of the Exchequer in 1735 and is regarded as an honest and able supporter of Irish interests. Outside parliament he is very active on boards, commissions and trusts, takes a hand in the building of Dr. Steevens’ Hospital and is pro-vice-chancellor of Trinity College Dublin. He lives in Belvedere House, now in the grounds of St. Patrick’s College, Dublin. He suffers from gout for a large part of his life.
From his father, Coghill, who never married, had inherited a lease from the Corporation of lands in Clonturk, where he erects a house which is afterwards known as Drumcondra House. He moves into Drumcondra House and lives there with his unmarried sister Mary until his death in 1738. He is buried in the family vault in St. Andrew’s Church, Dublin.
Upon Coghill’s death Mary is left, for her lifetime, his lands in the barony of Coolock, rents from his properties in Clonturk, all his household goods, and his coach, chariot and horses. In 1743, she erects the parish church of Clonturk, now Drumcondra Church, and places in it a statue of her brother by the Dutch sculptor Peter Scheemakers.