Marquess Conyngham, of the County of Donegal, is a title in the Peerage of Ireland. It was created in 1816 for Henry Conyngham, 1st Earl Conyngham. He was the great-nephew of another Henry Conyngham, 1st Earl Conyngham, a member of a family of Scottish descent which had settled during the Plantation of Ulster in County Donegal in Ireland in the early 17th century. The 'founder' of the dynasty in Ireland was The Very Rev. Dr. Alexander Cunningham, Dean of Raphoe. The earlier Henry was a member of both the Irish House of Commons and the British House of Commons and served as Vice-Admiral of Ulster and as Governor of the counties of Donegal and Londonderry. In 1753 he was raised to the Peerage of Ireland as Baron Conyngham, of Mount Charles in the County of Donegal, and in 1756 he was created Viscount Conyngham, in Ireland, also in the Peerage of Ireland. In 1781 he was made Baron Conyngham, of Mount Charles in the County of Donegal, with remainder to his nephew Francis Burton, and Earl Conyngham, of Mount Charles in the County of Donegal, which like the creations of 1753 and 1756 was created with normal remainder to the heirs male of his body. The latter titles were also in the Peerage of Ireland. Lord Conyngham was childless and on his death in 1781 the barony of 1753, the viscountcy and earldom became extinct while he was succeeded in the barony of 1781 according to the special remainder by his aforementioned nephew Francis. He was the eldest son of Mary, sister of the first Earl Conyngham, by her husband Francis Burton. The new 2nd Baron Conyngham, who had earlier represented Killybegs and County Clare in the Irish House of Commons, assumed by Royal licence the surname and arms of Conyngham on succeeding to the titles.

The Peerage of Ireland consists of those titles of nobility created by the English monarchs in their capacity as Lord or King of Ireland, or later by monarchs of the United Kingdom of Great Britain and Ireland. It is one of the five divisions of Peerages in the United Kingdom. The creation of such titles came to an end in the 19th century. The ranks of the Irish peerage are duke, marquess, earl, viscount and baron. As of 2016, there were 135 titles in the Peerage of Ireland extant: two dukedoms, ten marquessates, 43 earldoms, 28 viscountcies, and 52 baronies. However, these titles have no official recognition in the Republic of Ireland, with Article 40.2 of the Constitution of Ireland forbidding the state conferring titles of nobility and stating that an Irish citizen may not accept titles of nobility or honour except with the prior approval of the Irish government.