Dungan was the only son of William Dongan, 1st Earl of Limerick and Euphemia Maria, daughter of Sir Richard Chamber.
He was born in Jerez de la Frontera, Spain, but was naturalised by the Parliament of Ireland in 1654.
[1] His father ensured the family's support for James II of England following the Glorious Revolution.
[2] He was granted a commission in James' army during the Williamite War in Ireland, becoming colonel of Lord Dongan's Dragoons.
[3] As a result of Dungan's death, his father's earldom was inherited by special remainder by the first earl's brother, Thomas Dongan.