My GGG Grandmother was Winifred Concannon of Coosan Point, County Westmeath. I have spent considerable time going through the microfilmed records of St. Mary's Church in Athlone. From doing so I have learned the following:
Your William Concannon was the son of John Concannon and Mary Evers. They were married on 6/9/1878. William was the oldest of their 13 children. He was born on 2/11/1879. His godparents were Joseph Concannon and Mary Shine.
He married Catherine Mulvihill, the daughter of Martin Mulvihill and Elizabeth Benson, who was born on 2/18/1885. They had four daughters: Mary/Maura (b. 12/1/1911, sponsors: Joseph Concannon and Bridget Mulvihill); Elizabeth (b. 11/29/1914, sponsors: Patrick Concannon and Margaret Mulvihill); Ellen Christina (b. 12/17/1917, sponsors: Michael Concannon and Mary Concannon); and Catherine Frances(b. 2/15/1922, sponsors: Bernard and Elizabeth Mulvihill). Catherine married Martin Bailey on 8/7/194_(?). I am guessing these were your parents or grandparents.
William died on 5/30/1965 and is buried in lot A812 in Cornamagh Cemetery in Athlone. His wife Catherine's death is recorded as 5/12 with no year noted, but William was a widower when he died. Their daughter, Catherine Concannon Bailey, died 3/31/1984 and is buried with them.
I have much more information about the Concannons of Coosan and would be interested in anything you have learned since you first posted this message many years ago.