In Cork 1853 there were 396 Carroll's as tenants and 513 Casey's.
I think the easiest way to find their parents would be their birth records but both are common names. Daniel not as common as you would think. Do you have a close birth year for either.
The North East 1/2 of Cork belongs to a not for profit but
fee paying Irish History Foundation. The City of Cork is in the South West 1/2. A check of Daniel year ____? with a father James Carroll
could be one way of getting parents names as a birth record would have both parents names and mother's maiden names, parish/place and full date.
The names John and James would be the majority of given names and Daniel less so. An example would be from the census substitute the Griffith Valuation for Cork,
John 59, James 29, Daniel 15. (Patrick 29) Everyone thinks of the song Danny Boy as representing Ireland but it was one of the least used names, less than Matthew
I would look for the marriage in 1866. By 1866 civil registration had come into being. You can search with just their names. A marriage
record gives parish/place (usually the bridge's parish) both of their father's names,and date. Very occasionally you will get witnesses.
You should look to the www.irishgenealogy.ie
which should be the South-West 1/2 of Cork are listed there, if they aren't you can try the foundation. www.familysearch.org
has the civil records for Ireland which would start with the marriage and then any children born in Ireland!
marriage July 10, 1866 of John Carroll born 1845 age 21 to Mary Casey age 20 born 1846 CORK, Ireland
fa: James Carroll fa: Jeremiah Casey
LDS M70236-4 Ireland-EAsy 101499
Cork City or Cork Union, Cork City would be a Union town but would also have all parish's, townlands, villages and small towns within a 12 mile radius.
There are children listed but with US addresses and just
born Ireland, names same but location will tell you which
If they married in 1866 and left by 1870 they could of had at least 3 children by then.
Al John J.'s siblings were probably born 1830-50's and these would be all Parish records.
There are no census or census substitutes between the Griffith Valuation of 1853 www.askaboutireland.ie
1901/1911 Ireland Censuswww.census.nationalarchives.ie
No father's in the 1901 Census:
I went through directories and found several of each of the father's names but none listed were for Cork City, but Newtown, Kinsale and Skibereen.
boot & shoe marker, grocery, sail maker and cooper(barrel
maker)if these ring a bell I will give them too you. The are Carroll's in the City of Cork parish's but not Casey's so assuming born outside the city but still within the civil union (old poor law union) of Cork.
Based on the Union being Cork, there are two Jeremiah Casey's: This will be an example as I have no way to tell.
Jeremiah Casey, Parish of St. Finbar, Townland Ballinaspigbeg, Union of Cork, tenant of Anne Dennehy
Jeremiah Casey, Parish of Caherlag, Townland of Dunkettle
Union of Cork, tenant of Henry Mannix
There are 11 listings for James Carroll's in the civil registration area of Cork, Parish's
St. Anne Shandon
Too many to make any guesses.
You can contact me for the website for the Irish Foundation
if you are interested in persuing those email@example.com
(please put Foundation name in the
subject of your email)