I'm new to County Monaghan and the names therein.I am helping a friend, Bobby Skillen, trace his family ancestry and have received some info from another man who has provided information to us that coincides a bit with your information.
A Catherine McAvinney/MacAvinney was married on November 4, 1884, to a Hugh Skillen.The Parish of Newcastle, Church of Ireland, records indicate that Hugh and Catherine had 8 children between 1885 and 1899 in County Down.
There are three McAvinneys listed in County Monaghan on the Irish Flax Growers List, 1796:
Philip McAveany, Patrick McAveeney, and James McAvenie
From doing research on other names, these three men were probably related and probably should have the same spelling although which is correct would be hard to find out.
Do you or any others have this name or know of this name in County Monaghan?