Hi Tom,
Thank you for your message.
It can be difficult to find records without an exact place of origin as most Irish records sources are based on specific locations, usually a parish. The fact that you have a Michael Grogan in Pomeroy and Longfield is a good starting point to begin your search.
Civil registration did not begin officially in Ireland until 1864, so for birth record you will have to look in church records. Most Catholic records are still held locally, so you may want to write to the local parish priest for possible assistance. One websites that you may find useful is the Irish Times where they give an overview of what records are available in specific parishes.
For Pomeroy parish follow this link:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Tyrone&parish=Pomeroy&churchid=233
Longfield East civil parish is actually part of the Roman Catholic parish of Langfield. Here is the link ot see what records are available there:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Tyrone&parish=Langfield&churchid=364
You could also try searching for church records online:
www.familysearch.org have a large genealogical database that includes some birth and marriage records for Ireland.
www.rootsireland.ie has a vast collection of Irish church records, however you have to pay to use this website.
Alternatively, you could contact the Irish World Heritage Centre in Tyrone for assistance- they may have copies of church records. However a fee may apply for their services. Here are the contact details:
Irish World Heritage Centre,
51 Dungannon Road,
Coalisland,
Co. Tyrone.
B71 4HP
Phone: +44 28 8774 6065 EMail: info@irish-world.com
I hope that this is helpful. Best of luck with your research!
Kind regards,
Genealogy Support