Is he listed in with the other passengers and, if so, can you tell who he might have been travelling with? That is the only real lead I can think of. If he is listed separately at the end of the manifest, are there other Keatings or surgeons on board?
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Even if he had made it to the US, it would be unusual to find what part of Ireland he came from on a record. Sometimes a vital record of the person, a sibling, or their children will mention it, but not very often. The best hope for someone in that era would be a write up in a newspaper or a long obituary. Later the passenger records listed contact people in the country of origin, and naturalization records recorded more details for the place of birth, but 1850 is too early to hope for either.
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As for recording deaths of people who died at sea, I found these notes. So maybe he is recorded in the GRO for the Liverpool area.
https://www.nationalarchives.gov.uk/help-with-your-research/research-guides/birth-marriage-death-sea-or-abroad/------
from
https://www.familytreemagazine.com/records/vital/now-what-relatives-who-died-at-sea/Passengers who died en route were usually “buried” at sea, though sometimes (especially if the death occurred near the end of a voyage) bodies were kept on board and interred in a cemetery at the port of entry. In that case, you could find a gravestone and burial record.
As states began to require birth and death registration, they too included records of deaths on ships that arrived in their ports. So, someone who died en route to Baltimore, for example, might be found recorded in death records at Maryland’s state archives.
If the death occurred on a British-registered ship after the start of civil registration (July 1837 in England and Wales, January 1855 in Scotland, January 1864 in Ireland), a record had to be sent to the appropriate General Register Office (GRO) depending on the nationality or place of residence of the deceased’s father.
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from
https://www.familysearch.org/wiki/en/How_to_Find_New_York_Death_Recordsfor New York State, from 1847 to 1850 records were required but unpopular. But I would guess this didn't cover deaths at sea.