Hi Chris,
rootsireland.ie has the record of the marriage of William McEvilly in Mayo 1823.Wife's name is Mary.
There is also a record of a John McEvily born 1830 in Mayo but the parents aren't William and Mary.
There is a record of a birth of William Frank McEvilly with parents William and Mary born 1905 in Mayo.
rootsireland.ie is a pay site so you need to purchase the records in order to get the parish and the parents' names.
On ancestry.com Elaine Murray's public member tree has William McEvilly's birth as Waterford but I couldn't find the record on rootsireland.
However, I did another search on rootsireland.ie for William McEvilly with no year range specified and all counties checked and got 9 matches - 7 Mayo (M) & 2 Galway (G):
MacEvilly 1841 M MacEvily 1868 M MacEvilly 1868 M X2 McEvelly 1873 M McEvilly 1883 G McEvilly 1887 M McEvilly William Martin Galway 1900 McEvilly William Frank 1905 M
Elaine's tree also has Mary Foy as born 1812 Waterford which I found on rootsireland - it comes up as Mary Fea.
Mike Dunne's tree has William's birth as 1810 in Clare Island Mayo but it's not on rootsireland. Mike has William living in Lancashire in 1881!
There is no source supplied for the birth information but you might want to post to the Westport parish to see if anyone can verify the Clare Island info.
The Tithe Applotments (1823-27) which are free to search has 10 McEvillys in Mayo but none in Clare Island or Westport but you may want to check it out.
Col