I did a pretty extensive search for the marriage of Arthur Kennedy and Catherine Griffiths in both North and South Tipperary, as well as for the other counties in Ireland. I only found the marriage of an Arthur Kennedy and Catherine Griffiths recorded in Granard, Longford in 1835. But, this couple married in the Church of Ireland, not in the Catholic Church.
If Arthur and Catherine went across the River Shannon from Ballina, Tipperary, into Killaloe, Clare, the IFHF would not have a record of their marriage, as the IFHF have not indexed any records for County Clare to date.
I also checked for their marriage at the Latter Day Saints (LDS) website, but didn’t find it.
Don, you may want to consider going back to the IFHF website every few months and search for the marriage, as this organization is still in the process of acquiring birth, baptism, marriage, and death/burial records.