Thank you for your message. I hope that someone researching the same family makes a connection with you.
In the meantime, have you tried searching for records of James in the local church records in Magheralin parish?
Most Catholic records are held locally so you may need to write to the local parish priest for possible assistance. One website that you may find useful is the Irish Times where they give an overview of what records are available in specific parishes. It also shows you where copies of the records are available. For Magheralin parish, follow this link:
Most surviving Church of Ireland records 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. Here are their websites: http://www.nationalarchives.ie/ and http://ireland.anglican.org/about/42
Lists of these surviving registers can also be found at the National Library of Ireland.
You could also check for record of the family in the land acts pertaining to Ireland in the 19th century. There are two:
The Tithe Applotment Books (1823-1838) found at http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
and Griffith?s Valuation (1848-1864) found at http://www.askaboutireland.ie/griffith-valuation/
Have you tried looking in the 1901/1911 census records to see if there were any McGiveron?s still in the area at the time? They are available online here:
Some other websites that you may find useful 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
Genealogy links: http://www.genealogylinks.net/uk/ireland/down/index.html
Family Search: www.familysearch.org
The National Archives Scotland- family history: http://www.nas.gov.uk/familyHistory/
I hope some of this is helpful. Please be patient - as our programme has only begun to rollout across the island of Ireland and volunteers in some areas may not yet be organized.