County Mayo or County Galway: Dunn/Hogan/McDonough - Trying to locate birth or baptismal records

We are trying to locate the ancestors of Patrick Hogan (b1812 Ireland - d1874 England) and Catherine Dunn Hogan (b1834 to1836 Ireland - d1868 England). They migrated from Ireland to Newcastle upon Tyne, Northumberland, England sometime before 1855.  They were married; however, no certificate of marriage has been located.

We first see them in England in 1855 in son's birth record. The 1861 England census data indicates they are from Ireland. Also, in the 1861 census we see Julia Dunn McDonough (b1837 Ireland - d1914 England) living next door. We believe she may be a sister or cousin to Catherine. In the 1871 census data it indicates Julia and her husband Michael McDonough (b1826 Ireland – d1903 England) are from Galway.

DNA test from Ancestry indicate it is likely ancestors are from North and South of Galway, Galway and/or South Mayo. Another DNA connection of a possible Uncle to the Dunn sisters shows his marriage took place in Shrule parish.  ALSO DNA FAMILY TREES SHOW CONNECTION TO DUNNS IN OWER, KILLURSA, HEADFORD AND SHRULE.

I am trying to locate a birth/baptismal record for Julia Dunn (b1837) and Catherine Dunn (b1834-1836).  Any assistance would be appreciated!