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Fitzgerald and Dwyer are very common names in Tipperary and Limerick where you have posted. I searched for marriage records from 1867-1871 in Limerick and Tipperary where the bride and groom were Fitzgerald and Dwyer. I limited the records to the given names you mark as "probable". One record came up which is below.
I also looked for a James Burton birth record in 1875 and the only record available was in Co. Tyrone. Can you explain why the children were registered as Burton?
More specific info would be helpful. Thanks!