McCanns of Armagh - searching for birth parish

Searching for the birth parish of Lawrence McCann who was born about 1730 in County Armagh (supposedly) and died about 1814 in Virginia, USA.  He married a woman named Mary.  One of their children is supposedly James McCann.  James was born about 1750 in Ireland.  He married a woman named Ann Shields about 1787.  Some say that James was born in Dublin, like his wife, but I do not know the source of that information.  So, it is possible that Lawrence McCann did move to Dublin before the family went to North America.

Lawrence McCann's parents are rumored to be James McCann (b. abt 1710, Ireland; d. 1797, Virginia, USA) and Jane Hamilton (b. abt 1720, Ireland; d. 1798, Virginia, USA). 

Both Lawrence and James fought in the Pennsylvania militia during the Revolution, so they had arrived in North America by 1782 (the date their names appear in the militia rolls).

Any help would be most welcome!

Laura