surnamedb.com does not have information on the Downard surname, but familysearch.org shows Downards in Kent, England in 1600 and in London, England in 1588.
They were in Ireland in the 1600's
Moris Downing
Ireland Marriages, 1619-1898
marriage: 26 January 1661 Derry Cathedral, Templemore, Londonderry, Ireland
spouse: Frances Perkin
Anne Downing
Find A Grave Index
death: 1621
burial: Dublin, , County Dublin, Ireland
They were in Scotland in the 1500's
Johnne Downy
Scotland Births and Baptisms, 1564-1950
christening: 5 October 1589 , STIRLING, STIRLING, SCOTLAND
residence: Stirling, Stirlingshire, Scotland
father: Thomas Downy
mother: Cathrein Liddell
Johnne Downy
Scotland Births and Baptisms, 1564-1950
christening: 6 August 1587 , STIRLING, STIRLING, SCOTLAND
residence: Stirling, Stirlingshire, Scotland
father: Alexander Downy
mother: Marione Blakburn
Downy
Scotland Births and Baptisms, 1564-1950
christening: 7 January 1587 , STIRLING, STIRLING, SCOTLAND
residence: Stirling, Stirlingshire, Scotland
father: Johnne Downy
mother: Elezabeth Neilsone
Robert Downie
Scotland Births and Baptisms, 1564-1950
christening: 15 May 1589 , STIRLING, STIRLING, SCOTLAND
residence: Stirling, Stirlingshire, Scotland
father: Johnne Downie
mother: Elezabeth Neilsone
Jonet Downy
Scotland Births and Baptisms, 1564-1950
christening: 23 April 1590 , STIRLING, STIRLING, SCOTLAND
residence: Stirling, Stirlingshire, Scotland
father: Alexander Downy
mother: Marione Blakburn
Marion Dounie
Scotland Births and Baptisms, 1564-1950
christening: 27 April 1600 , FALKIRK, STIRLING, SCOTLAND
residence: Falkirk, Stirlingshire, Scotland
father: John Dounie
mother: Jeills Crossar
Jonet Downie
Scotland Births and Baptisms, 1564-1950
christening: 23 January 1596 , FALKIRK, STIRLING, SCOTLAND
residence: Falkirk, Stirlingshire, Scotland
father: Johne Downie
mother: Jeills Crossar
Jonet Downie
Scotland Births and Baptisms, 1564-1950
christening: 30 April 1587 , STIRLING, STIRLING, SCOTLAND
residence: Stirling, Stirlingshire, Scotland
father: Duncane Downie
mother: Margaret Wilsone
Charlis Downie
Scotland Births and Baptisms, 1564-1950
christening: 17 June 1576 SAINT NICHOLAS, ABERDEEN, ABERDEEN, SCOTLAND
father: Andro Downie
mother: Marione Joniston
Bessie Downy
Scotland Births and Baptisms, 1564-1950
christening: 12 June 1586 MONIFIETH, ANGUS, SCOTLAND
father: Jhonne Downy
Alexr. Downy
Scotland Births and Baptisms, 1564-1950
christening: 7 February 1579 MONIFIETH, ANGUS, SCOTLAND
father: Jhone Downy
Jonet Downie
Scotland Births and Baptisms, 1564-1950
christening: 23 January 1596 , FALKIRK, STIRLING, SCOTLAND
father: Johne Downie
mother: Jeills Crossar
Violet Donyng
Scotland Births and Baptisms, 1564-1950
christening: 17 November 1566 PERTH, PERTH, SCOTLAND
father: Robert Donyng
Christane Donyng
Scotland Births and Baptisms, 1564-1950
christening: 26 October 1561 PERTH, PERTH, SCOTLAND
father: Dauid Donyng
Patrik Donyng
Scotland Births and Baptisms, 1564-1950
christening: 2 May 1563 PERTH, PERTH, SCOTLAND
father: Robert Donyng
Jonet Downie
Scotland Births and Baptisms, 1564-1950
christening: 30 April 1587 , STIRLING, STIRLING, SCOTLAND
father: Duncane Downie
mother: Margaret Wilsone
Jonet Downy
Scotland Births and Baptisms, 1564-1950
christening: 23 April 1590 , STIRLING, STIRLING, SCOTLAND
father: Alexander Downy
mother: Marione Blakburn
Downy
Scotland Births and Baptisms, 1564-1950
christening: 7 January 1587 STIRLING, STIRLING, SCOTLAND
father: Johnne Downy
mother: Elezabeth Neilsone
James Downy
Scotland Births and Baptisms, 1564-1950
christening: May 1590 STIRLING, STIRLING, SCOTLAND
father: Duncane Downy
mother: Margaret Wilsone