Hi Robert,
Thank you for your message.
Civil registration did not begin in Ireland until 1864 so prior to this all records of births, marriages and deaths were kept by the local parish church so this is where you will need to go to find information on Alexander and Ann?s parents. If you can find their baptismal cert it will have this information, also if you can find their marriage cert it may have their fathers? names listed.
Unfortunately, Catholic records for the area do not begin until 1863. You can see this at the Irish TImes website:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Tyrone&parish=Termonamongan&churchid=342
Church of Ireland records generally tend to have an earlier start date so if they belonged to this church you may have a chance of finding these records. 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.
It may also be an idea to contact the Irish World Heritage Centre to see if they can offer you any assistance, however a fee may apply. Here is their email: info@irish-world.com
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.
Kind regards,
Genealogy Support
