I’m also looking for the Patrick Murphy family. He was born March of 1874
Cathy, I am looking at old queries and yours is tricky as that is a common name, civil records are available free on line from 1864 and ayou can now search them but with out the registration district in Cork you probably get a lot but the parents names should be on the certificate entry, also church reocrds for Cork are on the same free site but you must sign in.
https://www.irishgenealogy.ie/en/ Click on either civil or church as you prefer, not all births were registered but bapism was a must.
Good Luck
Pat