Thank you for your message.
Have you tried looking in Church records for information on the family? Most Catholic records are held locally. One website which may be helpful is the irishtimes. Here they give an overview of what records are available in specific parishes. For Portadown/Drumcree parish follow this link:
For Church of Ireland records go to http://www.ireland.anglican.org/index.php?do=information&id=63
You could also check Griffith's Valuation for some mention of him. This was a property Valuation survey carried out between 1848-1864. You can search this here:
If you can find William or Margaret's parents names, you could search for them in the ealrier land record called the Tithe Applotment Books (1823-1838) here:
Do you have any other information on the family? For example, did they emigrate and if so what do you know of their emigration? If some of the family remained in Ireland you may be able to find them in the 1901/1911 census records. You can check these here:http://www.census.nationalarchives.ie/search/ Some other websites which may be helful 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
Alternatively toy could try contacting Armagh Ancestry, however a fee may apply. Here are their contact details:
40 English St.,
Phone: +44 28 3752 1800 Email: firstname.lastname@example.org
I hope this is helpful. 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.