Cole was the son of Sir John Cole, 1st Baronet, by Elizabeth Chichester, daughter of Lieutenant-Colonel John Chichester and the Honourable Mary Jones, daughter of Roger Jones, 1st Viscount Ranelagh, and aunt of Richard Jones, 1st Earl of Ranelagh.
He succeeded his father in the baronetcy in c. 1691 and was returned to the Irish House of Commons for Enniskillen in 1692, a seat he held until 1695. From 1695 to 1703 he represented Roscommon Borough in the Irish Parliament.
Lord Ranelagh was twice married.
Both marriages were childless. He died in October 1754 when the baronetcy and barony became extinct.
