Peter,
The townland where Patrick was living when he married was Fofannybane. It’s also where he died. His father Owen was alive in 1829 because he is listed in the tithe applotment records for that townland:
http://www.irishgenealogyhub.com/down/tithe-applotment-books/kilcoo-parish.php
I searched Griffiths Valuation (1863) for Fofannybane and Owen was not listed then suggesting he had died.. There were 4 Fitzpatrick properties in the townland. Plot 2a was Catherine with 3 acres. She was subletting a cottage to Francis on 2b. Next door on 3 was John Fitzpatrick with another small farm. On plot 19 was Henry with another small farm. I followed the occupants forward using the Valuation revision records on the PRONI website. Catherine died in 1883 aged 80. She was a spinster:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1883/06347/4820969.pdf
She was replaced by Patrick, so presumably there was a family connection there. Possibly she was an aunt?
Henry died in 1872 aged 70. His wife was still alive. The informant was Mary Ann so possibly that was her. John died in 1875 aged 80. A bachelor. I’d suspect a family connection to Catherine and Patrick since his farm was next door. A brother to Owen perhaps?
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…
This looks to be Patrick senior in the 1901 census. His age then suggests a birth c 1845 (ages on censuses and death certificates in the 1800s were often just guesses. They could easily be out by up to 10 years for someone in their 60s or older):
http://www.census.nationalarchives.ie/pages/1901/Down/Tofanny/Tofannyba…
Fofannybane is in the RC parish of Maghera. Sadly their baptism and marriage records only start in 1845. Patrick was born around 1835 – 1845 and so, assuming that’s where he was baptised, if it was before 1845 there are no records to search. I cannot find a baptism for him and so assume he was born before 1845.
Most RC parishes don’t keep burial records. However Maghera does have them for 1860 – 1882. I searched on Ancestry but did not find Owen so assume he died before 1860. Statutory death registration only started in 1864 so you won’t find a death certificate for him either.