The title of Marquess Conyngham (pronounced "Cunningum")was created in the Peerage of Ireland in 1816.

The Marquess holds the subsidiary titles of Earl Conyngham (1797), Earl of Mount Charles (1816), Viscount Conyngham (1789), Viscount Mount Charles (1797), Viscount Slane (1816), Baron Conyngham (1753), and Baron Minster (1821), all in the Irish Peerage except the last, a U.K. peerage.

The Marquess sat in the House of Lords before the passage of the House of Lords Act 1999 as Baron Minster.

Barons Conyngham (1781)

• Henry Conyngham, 1st Earl Conyngham (1705-1781)
• Francis Pierpoint Conyngham, 2nd Baron Conyngham (d. 1787)
• Henry Conyngham, 3rd Baron Conyngham (1766-1832), created Viscount Conyngham in 1789 and Earl Conyngham in 1797, elected a Representative Peer in 1800, created Marquess Conyngham in 1816 and Baron Minster (UK) in 1821

Marquesses Conyngham (1816)

• Henry Conyngham, 1st Marquess Conyngham (1766-1832)
• Francis Nathaniel Conyngham, 2nd Marquess Conyngham (1797-1876)
• George Henry Conyngham, 3rd Marquess Conyngham (1825-1882)
• Henry Francis Conyngham, 4th Marquess Conyngham (1857-1897)
• Victor George Henry Francis Conyngham, 5th Marquess Conyngham (1883-1918)
• Frederick William Burton Conyngham, 6th Marquess Conyngham (1890-1974)
• Frederick William Henry Francis Conyngham, 7th Marquess Conyngham (b. 1924)