Hi! Roger asked me to look at your query, because my grandparents grew up in that area (although I live in the US). As it happens, my maternal grandmother grew up just a few townlands west of Carrowliam, in the townland of Callow. I also happen to have some Moran relatives on my grandfather's side, but from a different (though nearby) parish, Killedan, where a Mary Moran married one of my mother's first cousins in 1910.
As you may already know, the parish records of baptisms for Killasser which are available online start too late for any record of John Moran in 1843, and end before your grandfather was born, but I was able to locate the record of the marriage of John Moran and Bridget Gildea in 1872 (attached), as well as the baptism of their older (eldest?) son John in 1876 (also attached). I also found a marriage record for a John Moran and a Bridget Sheridan in 1876, and the baptism of their son Michael the same year (both attached). The Moran-Sheridan family lived in a different townland (which I can't decipher), but the two John's might well have been cousins.
Although I can't provide any other info about your immediate Moran family, I can provide some about the parish. There was a history book published in 2011 in Ireland, entitled “Killasser: Heritage of a Mayo Parish”, which contains lots of information about the area. The author was Bernard O’Hara, who was apparently working with the Killasser/Callow Historical Society. It can sometimes be found on Amazon, and The ISBN is 978-0-9850753-1-6. It is also available for downloading on Kindle readers, at a very reasonable price. Killasser is the name of both a Catholic parish and a “civil parish”. Civil parishes were once church-related, but evolved into administrative districts, and their boundaries (and often their names) are not always the same as those of the local Catholic parish. More about the civil parish of Killasser is available at this link: https://www.townlands.ie/mayo/killasser/
At that web site, there is also a separate page about Carrowliam More, which you can reach directly at this link: https://www.townlands.ie/mayo/gallen/killasser/tumgesh/carrowliam-more/
There are further links there to the 1901 and 1911 censuses, as well as Griffiths Valuation. Here's a direct link to the 1901 census record:
https://www.census.nationalarchives.ie/search/results.jsp?census_year=1901&county19011911=Mayo&townland=Carrowliam%20More&ded=Tumgesh&search=Search
There's only one Moran family shown for that year (see page 1), which is almost certainly yours, since the father is named John, and is of about the right age, with a son named Michael who is also about the right age, from what you have indicated. The mother is not listed, so she may have died by then. John and Michael are also both listed in the 1911 census, which you can access here (see page 6):
https://www.census.nationalarchives.ie/search/results.jsp?census_year=1911&county19011911=Mayo&townland=Carrowliam%20More&ded=Tumgesh&search=Search
In Griffiths Valuation (mid-1800's), there is only one Moran tenant listed, a James Moran. He was likely the father of your John Moran, so that takes you back another generation. You can see that record here:
https://www.askaboutireland.ie/griffith-valuation/index.xml?action=doNameSearch&PlaceID=969413&county=Mayo&barony=Gallen&parish=Killasser&townland=%3Cb%3ECarrowliam%20more%3C/b%3E
The Moran surname (Ó Moráin or Ó Moghráin in Irtish) is more common in Mayo than anywhere else in Ireland. You'll notice in the records I've indicated that there are also a number of people surnamed Morran, Morren, Marrin, and even Marn, which are less common names in Mayo, and are normally anglicized forms of a different surname, Ó Mearáin, but the anglicized forms of names were often very inconsistent, so some may originally have been Ó Moráin or Ó Moghráin.
A final info source which might interest you is a web site in Ireland which can be helpful to people who have identified a particular parish as relevant to their family history. In the 1930’s, Irish schoolchildren were sent out on class projects where they interviewed mostly older people in their parish about the history and customs of the area. Over 250,000 interviews were conducted and they are available online at the Irish National Folklore Collection Project’s site:
https://www.duchas.ie/en
The content of the interviews varied from place to place, but they can cover local history, local place names, people known to the person being interviewed, local myths and superstitions, and other customs, such as how holidays or weddings were celebrated and even on what day of the week people customarily did their washing or baked bread. It’s said to be the largest national folklore collection in the world, and the interviews can be fascinating. Some of the interviews were conducted in English and some in Irish. My grandparents grew up speaking Irish at home, and it's likely that your grandfather did also, since he was born not long after my grandparents were. The children would have spoken English at school, however, as the use of Irish was normally strongly discouraged there. I learned some Irish from my grandmother,and have studied it further here and in Ireland, and it is making a decent comeback in Mayo these days..
Slán!
Kevin