Ballaly would be have been a bit borderline with regard to which parish it was in, but during the 1880s most likely be in Dundrum, but might also be worth checking Sandyford. For earlier dates the area was part of the RC parish of Booterstown (I think Dundrum was founded as a parish in the 1850s).
Unfortunately the RC records for Dundrum dont include death/burials. There is St. Nathi's graveyard near William Dargan (Luas) bridge and Joe Daly's - most of the burials there are Church of Ireland. I dont see any other graveyards that close to Dundrum or Ballaly. The nearest would probably those used by Sandyford parish - i.e. Kilgobbin, Kiltiernan etc, or maybe Dean's Grange which opened in the 1860s..
You can check details of County Dublin cemeteries on the Dublin City Library website at :
http://dublinheritage.ie/graveyards/browse.php Shane