He was a student at Queens' College, Cambridge from 1750 and in turn at Lincoln's Inn from 1753, he then proceeded to follow a military career, being commissioned as a Captain in 1759, and by 1769 he had advanced to Lieutenant-Colonel in the 12th Dragoons.

He resigned his Regular Army commission in 1774,[2] but in April 1793 he was appointed Colonel to raise and command the new Prince of Wales's Own Donegal Militia.

[2] Conyngham planned a settlement on the previously unpopulated island of Rutland, Ireland, having installed, from 1784, a street of residences and business premises, post office, school house and a fish landing and processing facility.

The village which developed around the mainland pier which served Rutland, Burtonport, still bears his name.

[4] In 1785 Conyngham commenced the building of Slane Castle, assisted by his nephew the 1st Marquess Conyngham, on a site overlooking the River Boyne just a few kilometres upstream from the site of the Battle of the Boyne.