First of all, do you know what religion they were?
There are Roman Catholic church records available for the diocese of Lissan (Armagh). These date from 1823 for baptismal records and 1839 for marriage records. You can find these at the National Library of Ireland, Pos. 5585, or the Public Records of Northern Ireland (PRONI), MIC.1D/36. If you have any difficulty, you could try writing to the parish priest for more assistance.
Church of Ireland parish registers for the period up to 1870 are public records. Registers are available for about one third of the parishes, however many were destroyed in the Public Records Office in Dublin in 1922. Most are still held by the local clergy, although some are in the National Archives of Ireland and others are in the Representative Church Body Library in Dublin. A list of all surviving registers is available in the National Archives.
Civil registration records are available from the General Register Office (GRO). These start from 1864 however. You can access the website here: http://www.groireland.ie/research.htm
You could also try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffith's Valuation (1848-64). Griffith's is freely available here: www.askaboutireland.com or here: www.failteromhat.com Failte Romhat has lots of other useful links you could try looking at.
Please make sure you link anyone else in your family who is interested in their Irish heritage to our site - and indeed anyone else you know of Irish heritage.
Genealogist (Ireland XO)