It appears that you have two families confused with each other. My first question and probably the most important one pertains to Patrick's death certificate in 1922.
Do you have an actual death certificate for Patrick? Does it show the mother's maiden name. If it shows that Ellen Nolan is the mother then the following family is the one your interested.
The family of John Sugrue and Ellen Nolan were located in Loughnagore, Killeentierna, County Kerry. The Civil Parish of Killeentierna is in the Catholic Parish of Killeentierna and it's located in the Registration District of Tralee. Location of Killeentierna is east of Dingle but quite to County Cork.
John and Ellen had the following children born to them and through my experience the first Mary and Patrick died young thus the renaming of those children on the later births.
Bridget born Sep. 12, 1828
Patrick born Feb. 7, 1830
Denis born Aug. 8, 1832
Mary born Dec. 20, 1834
Mary born May 27, 1837
John born Mar. 26, 1841
Patrick born May 20 1843
If your Patrick is from this family and he was born in the 1840's then his birthday was May 20, 1843.
The Ireland, Civil Registation Death Index 1864-1958 shows the following two possibilities. Don't disgard them and don't count them until you can prove they are the ones you are looking for. My guess is that they are based on the first child born. I suspect that John Sugrue and Ellen Nolan would have married around 1825-1826.
John Sughrue died 1867 at the age of 65 showing a birth year of 1802. The Registration District is Tralee and it can be found in Volume 15 on Page 368 should a request be made to the General Registrars Office.
Ellen Sughrue died Jul-Sep 1883 at the age of 80 showing a birth year of 1803. Her death can be found in Vol 5 on page 377.
I made request similar to the above ones based on the area, approximate ages, deaths, and obtained my correct ancestors death records. Again don't rely on them to be correct till proven.