Lords of Ireland (1171-1541)
Henry II, Lord of Ireland (1171 - 1189)
Richard I (1189 - 1199)
John (1199 - 1216)
Henry III (1216 - 1272)
Edward I (1272 - 1307)
Edward II (1307 - 1327)
King Edward Bruce (1315 - 1318) (Edward Bruce in opposition to Edward II)
Edward III (1327 - 1377)
Richard II (1377 - 1399)
Henry IV (1399 - 1413)
Henry V (1413 - 1422)
Henry VI (1422 - 1461 and 1470 - 1471)
Edward IV (1461 - 1470 and 1471 - 1483)
Edward V (1483)
Richard III (1483 - 1485)
Henry VII (1485 - 1509)
Henry VIII (1509 - 1542)
Kings/Queens of Ireland (1541-1649)
Henry VIII, King of Ireland (1542 - 1547)
Edward VI (1547 - 1553)
Jane Grey (1553)
Mary I (1553 - 1558)
Elizabeth I (1558 - 1603)
James I (1603 - 1625)
Charles I (1625 - 1649)
Lord Protectors of the Commonwealth of England (1649-1660)
Main article: English Interregnum
Oliver Cromwell (1649 - 1658) (Lord Protector)
Richard Cromwell (1658 - 1660) (Lord Protector)
Kings/Queen of Ireland (1660-1801)
Charles II (1660 - 1685)
James II (1685 - 1688)
William III (1689 - 1702) and Mary II (1689 - 1694)
Anne (1702 - 1714)
George I (1714 - 1727)
George II (1727 - 1760)
George III (1760 - 1801)
Kings/Queen of the United Kingdom of Great Britain and Ireland (1801-1927)
George III (1801 - 1820)
George IV (1820 - 1830)
William IV (1830 - 1837)
Victoria (1837 - 1901)
Edward VII (1901 - 1910)
George V (1910 - 1927)
Kings of Ireland (1927-1949)
George V (1927 - 1936)
Edward VIII (1936)
George VI (1936 - 1949)
King/Queen of the United Kingdom of Great Britain and Northern Ireland (1949-Present)
Continues to rule in Northern Ireland after Republic of Ireland was declared in 1949
George VI (1949 - 1952)
Elizabeth II (1952 - Present)
The above is a bit confusing, so you might wish to visit http://en.wikipedia.org/wiki/King_of_Ireland for more info and additional references.
best of luck to you!