Thank you for your message.
Do you know what parish in Co. Armagh the family belonged to? Do you have any documentation that mentions a townland/parish/village/town?
The main source of records for the timeperiod are church records, however most of these are held locally. So as you can imagine if you could find their parish it will be much easier to find their records.
Do you know much about their emigration? Generally more information was given at the port of arrival rather than that of departure. If you knew where they entered Canada it may be a place to find more information-and maybe even an exact place of origin. For the National Library and Archives of Canada, follow this link:
There are a few websites where you could run their names and hopefully you might get some results:
Both Catholic and Church of Ireland records are currently being uploaded at www.irishgenealogy.ie/index.html free of charge. However as this is an ongoing project not all records are available yet.
The two land records pertaining to Ireland in the 19th century;
The Tithe Applotment Books (1823-1838) at http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
Griffith's Valuation (1848-1864) found at http://www.askaboutireland.ie/griffith-valuation/
Finally, family search at https://familysearch.org/
Some other websites which may help in your research are:
The National Archives of Ireland http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
The National Library of Ireland http://www.nli.ie/en/family-history-introduction.aspx
The National Archives UK ? genealogy search: http://www.nationalarchives.gov.uk/records/looking-for-person/
The Public Records Office of Northern Ireland http://www.proni.gov.uk/index/family_history.htm
I hope that these help. Remember to post any new information that you find as the more information you post, the more likely it is that one of our volunteers will be able to advise or assist you. Also include information concerning which sources you may have already used so others may further your search.