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.
His son was captain Walter Cuney, a Parliamentary officer under Colonel Rowland Laugharne in Pembrokeshire in 1643.