I don't know how much this will help you, but there was a Patrick
Cunningham living in
Granville Township in 1801. This was very likely the father of your Patrick, as there weren't a lot of people around that early.
From The
Welsh Hills by William Harvey Jones:
"The third cabin built on the
Hills was that of David Lewis, erected in the late fall of 1802. Although Lewis was employed and lived in
Newark, he found time to build his cabin with the help of Patrick
Cunningham and his sons, who had settled on the old
Munson farm east of
Granville in 1801. "