I think you meant to address your post to "Annie" rather than "Stephanie" ?
Per civil registration indexes, Hugh Skillen & Catherine McAvinney married in 1884 in Kilkeel parish, Co. Down. If you have their marriage record, it listed their fathers' names and their residences, which were probably towns or townlands in Kilkeel parish. So you do know the Skillen and McAvinney name (at least each father) in the generation before Hugh & Catherine.
If you don't have their complete marriage record, you canget it on-line from a web site such as Irish World or Emerald Ancestors.
So, are you backtracking to find ANY earlier Skillens and McAvinneys, and so searching in Monaghan? Or do you have a specific family connection for Hugh and Catherine in Co. Monaghan?
Griffith's Valuation shows a number of SKILLENS in Kilkeel parish, Co. Down, including HUGH SKILLEN in Ballyveagh More townland. I haven't traced any of those families, just noted that the name does occur a lot in Co. Down and may connect to the supposed Skillen wife of John Finlay in Co. Monaghan. Hopefully I'll know more when I've located some of these families (children, grandchildren, or whoever) in the 1901 census.
On McAvinney (with many spellings), I'm not sure of the possible connection of "Philip McAveany, Patrick McAveeney, and James McAvenie" in Co. Monaghan in the 1790s to your Catherine McAvinney nearly 100 years later in Co. Down. "Patrick" is almost certainly Catholic, while Philip and James could be either Protestant or Catholic (though Philip sounds more likely to be Protestant). If they were all of one religion, I'd say yes, they were most likely related, but if they were NOT the same religion, kinship is much less likely. Do you know if your Catherine was Catholic or Protestant? It will make a big difference in tracing her family.