Unfortunately I couldn't find any Cuffes or Cafferkeys in the irish phone book.
Howver here's a copy of the marriage record from www.rootsireland.ie/ which has the fathers' names:
Date of Marriage:14-Feb-1883
Parish / District:KNOCKNALOWER DISTRICT
20Status:Bachelor (Previously unmarried)
Spinster (Previously unmarried)
THEY WERE MARRIED IN THE CHAPEL OF KILCOMMON ERRIS BY THOMAS DOLPHIN.
Do you need further assistance to go back further from Michael & Mary?
Col Cafferky Achill Parish Contact