In the 1860 ‘s in
www.askaboutireland.ie/griffith-valuation/indexThere are no Tihney
there is one Tiney Co Donegal
there are 2 Patrick Tinney and more other Tinney in Co Antrim, Donegal, Limerick Tipperary, Tyrone,
In the irish Census 1911
www.census.nationalarchives.ie/search/there are Tiney in Co Donegal
there are 11 Patrick Tinney and more other Tinney in Co Antrim, Donegal, King's Co, Cavan, Limerick, Londonderry Tipperary, Tyrone,
There are no Owen unless it is a second first name in either above
Trying familysearch.com, there are no Tihney. But it has
OWEN TINNEY Birth: 10 OCT 1870 , Donegal, Ireland
Parents:
Father: THOMAS TINNEY Family
Mother: FRANCES MC DERMOTT
And from the USA census 1880
Owen TINNEY Self M Male W 50 I, and family living in NY So This OWEN Tinney was b abt 1830
Also familysearch.com has many Patricks
Wishing you every success further, Jim