Somehow I didn't see a single DOB, DOM, or placename in your post. These things help.
I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For Morgan Cregan B ???? in Newcastle West, Co. Limerick, with the father's forename unknown, I found 2 rcds: 1824 and 1871. Father's forenames were Morgan and James respectively.
For Morgan Cregan M ???? in Newcastle West, Co. Limerick, I found 1 rcd in 1845. Assuming the B rcd from above is correct, this 1845 DOM would be just about right. A view of the detailed rcd SHOULD show the bride's full name and their parents' names as well as other info.
For most of the children, with a father forenamed Morgan, I found 0 rcds in all of Ireland within the database. For those where I found rcds, none were in a relevant range of yrs. Are you sure they were born in Ireland and not in America?
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.