Hi Carole,
Thank you very much for your message. I hope that someone with information on Alexander makes a connection with you and helps you to further your research.
As civil registration did not begin until 1864, you will need to look in church records for information on his birth. Do you know what religion the family were?
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 Moira/Magheralinn parish, follow this link:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Down&parish=Magheralinn&churchid=438
Unfortunately, as you can see from the above link, records for the parish do not begin until 1815.However, in the19th century new Catholic parishes were created so starting dates can sometimes be misleading. Many parishes changed their geographical spread so you may find earlier records relating to your family in the records of adjoining parishes:
http://www.irishtimes.com/ancestor/browse/counties/rcmaps/downrc.htm
Church of Ireland records generally tend tyo have an earlier start date as it was the official church of the country. 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.
Some other websites that you may find 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: www.familysearch.org
Genealogy links: http://www.genealogylinks.net/uk/ireland/down/index.html
From Ireland: http://www.from-ireland.net/county-down-genealogy/
Roots Ireland: www.rootsireland.ie (please note you have to pay to view records on this site)
All the best,
Genealogy Support
