Richard Cuney or Cuny (died bef. 24 October 1627) was a Welsh politician who sat in the House of Commons from 1604 to 1611. He was the son of Walter Cuny of Lamphey, Pembrokeshire. As a soldier he was a captain of Foot in the Lisbon expedition of 1589, the Normandy campaign of 1591, in Guernsey in 1593 and in Ireland in 1595, 1597. He was a lieutenant colonel on the Cadiz expedition of 1596 and a full colonel and serjeant-major of the army in Ireland in 1598. In 1604, he was elected Member of Parliament for Pembroke. He was appointed High Sheriff of Pembrokeshire for 1614–15.