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I searched the subscription site Roots Ireland and did not locate a marriage record for Catherine Burke and Roger Moraghan anywhere in Ireland. Many RC parishes do not have records back to 1833 and before.
Looking at the Tithe data, most Moraghans were found in parishes in North Roscommon and not on the border with Co. Galway. My guess is that the couple likely met and married in Birmingham.
You may want to add Catherine and Roger's emigration story to our XO Chronicles site and possibly someone will see a connection https://www.irelandxo.com/ireland-xo/history-and-genealogy/ancestor-data...
Have you considered DNA testing?