Geoff,
I found William's death on the irishgenealogy website. You can view deaths in Tyrone there from 1878 to 1921 (free). For deaths 1864 to 1877 you have to use the GRONI website which charges £2.50 (sterling) to view the certificates.
I searched for deaths for Cornelius 1864 - 1901 but did not find any, suggesting either that he had died before 1864 or left Ireland. I also searched for deaths for Ann for the same period. I only found one in Tyrone that would fit. She died 29.8.1877 aged 89, registered in Cookstown. (That's some distance from Ardstraw so possibly not your family).
I looked in Griffiths Valuation for Tyrone c 1860. No Cornelius Cory/Corey listed suggesting again that he wasn't living in Tyrone at that time. If Cornelius & Ann died pre 1864, then there will be no death certificates as they were only introduced that year. Catholic parishes rarely kept burial records so thatalso makes them hard to find.
If I have understood correctly, Cornelius & Ann had Catherine in 1820 and Michael in 1851. That's a span of 31 years. Most women weren't fertile that long in the 1800s. The average family spans 20 - 25 years max. In my opinion, either the ages aren't right or Cornelius had remarried. Very few Catholic parishes in Tyrone have baptism or marriage records for the late 1700s/early 1800s, so you may struggle to find a record of their births or marriage.