I was hitting a brick wall trying to get the information for James birth records in Ireland or immigration dates. Using the correct birthdate should help.
Baptism records, as previously noted, not birth are what you seek, could be a week, month or year after.
Emigration records were not kept. Immigration records (passenger lists) should always be sought in the destination country.
https://www.irish-genealogy-toolkit.com/Irish-emigration.htmlEvery one of my father's family was Episcopalian so their religion maybe the Church of England.
If your family were Episcopalian then all the R.C. baptisms online (with variable start dates, some as late as the 1860's) are pointless to search. Church of
Ireland records may or may not exist but if they do unlikely to be on Ancestry or Familysearch. Need to name search on RootsIreland.
https://www.rootsireland.ie/ Some
Dublin and Cork C of I baptism records are on
https://churchrecords.irishgenealogy.ie/churchrecords/Many (60% of the parishes) are lost, destroyed 1922. By 1922 the records of 1,006 parishes in Ireland had been deposited in the Public Record Office in Dublin, leaving the records of only 637 parishes in local custody.
https://www.irish-genealogy-toolkit.com/trace-ancestors.html For those that survive by no means all parishes are transcribed on RootsIreland, and they have concentrated on the 1800's rather than the 1700's as that is what the majority seek. Some are still in local custody. For Northern Ireland most registers were photographed 1960's but the images have to be browsed on microfilm in PRONI, Belfast so a prior knowledge of the church/parish is essential if one of the ones not name indexed on RootsIreland.
https://www.irish-genealogy-toolkit.com/church-of-ireland-records.html9/2/1881 if you are American
Better off all typing 2 Sep 1881 or Sep 2 1881 and avoiding US-UK ambiguities altogether, hence (d)d mmm yyyy being the tree input format suggested by Ancestry, MyHeritage, FamilySearch and gene bloggers etc.
d mmmm yyyy was the style used for that page of the New Orleans death register.