I think John & Mary married in Ashby de la Zouch, Leicestershire, Apr – Jun 1867 Volume 7a, page 203. That certificate should give the couples fathers’ names and occupations which may help get back a little further. If they met in England, then of course they may well come from different parts of Ireland.
There are no birth certificates in Ireland prior to 1864 so you’ll be reliant on church records. So I need to know their denomination. I’d guess Mary was RC but Moffatt in Ireland is often a Protestant name, so he might not necessarily also be Catholic. Do you know what precise denomination he was?
If either was still alive in England in 1911, check that census. In that particular year people often put more than “Ireland” as their place of birth. You sometimes get a town or parish.