Hi Judy,
Thank you for your message.
Do you know where in Ulster Gordon was born? One of the main pieces of information that you need when researching your family history in Ireland is a location. Most Irish record sources- church records, land records, census records- are based on specific locations. Until you know a specific location within Ireland, preferably a parish or placename, it may be difficult to do anything more with these records.
If he was born in Armagh parish, in Co. Armagh, you can see what Catholic records are available in the parish on the irishtimes website. Here is the link:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Armagh&parish=Armagh&churchid=184
To check Church of Ireland records go to http://ireland.anglican.org/about/42 and http://www.nationalarchives.ie/.
If you are unsure what parish he was born in, perhaps you could try looking into his emigration. Generally more information was given at the port of arrival rather than that of departure. If you knew where he arrived in Canada, it may be a place to find more information-and possibly even an exact place of orign. For immigration information in Canada check the National Library and Archives at the following site: http://www.collectionscanada.gc.ca/index-e.html
Some other websites which may be helpful 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
Family Search: https://familysearch.org/
Genealogy Links: http://www.genealogylinks.net/uk/ireland/armagh/index.html
Remember to post as much information as you can with regard to the people you are researching. 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.
Kind regards,
Genealogy Support