Martin Fleming and Mary (Haverty) Fleming

I have been searching, for several weeks, for links to Loughrea, Galway about my g/g grandparents. Their gravesite in Fairmont, W.V. (USA) states they were both born in Loughrea, Co. Galway. In looking at naming patterns, I suspect Martin's father was named Patrick Fleming, and Mary's father was James Haverty. I deducted this from their first 2 sons being named Patrick William Fleming and the second son James H. Fleming. I have census data for this family from 1860 onward in the US. In searching parish by parish in the Griffith valuations, I have discovered only Boyounagh parish has a James Haverty, and a Patrick and Martin Fleming. I believe Martin Fleming (1820) and Mary Haverty (1825) were both born in Loughrea but there families moved to Boyounagh at some point.

Martin and Mary's first child Anna E. Fleming (1850) and  second child Patrick W. Fleming (1852) were both Irish born. In 1855 there were no Fleming's or Haverty's listed for Loughrea parish. I need to find Birth records in Loughrea in 1820-1825 for them, or marriage records in the 1845-1850 in either parish.

  This family was RC and are buried in a catholic cemetery here in West Virginia. I believe they immigrated in late 1855 or Jan of 1856. second son (third child) James H. Fleming was born in Virginia (now West Virginia) 22 Jan. 1856.

I have a birth date of 11 nov 1850 for child Anna E Fleming and just the year 1852 For Patrick William Fleming. These are from family history and are not confirmed by record. A link to their birth place could be either parish, as it proceeds the Griffiths time frame.

Thanks

James D Fleming (named for my paternal grandfather)