Researching the surname COUNTY

Michael COUNTY m Anastasia/Antice Manton Tipperary Ireland
having a family name of County is very very difficult, as I get all the (county's in Ireland USA not surnames )
also names like ......
Mc Carthy,Ryan,Murphy, are very common and every second one is Mary,Catherine,Patrick, James or John etc...
I have all bmd certificates to date
My father was Tom County b1912-1988 son of John Michael County son of
James County m Catherine Mc Carthy 26/1/1860 ( My gg parents ) who married in Adelaide South Australia 1860 however we cannot find any trace of
either James or Catherine coming to Australia !!!
this seems to be the problem we know that the came from Thurles area Tipperary Ireland and they were
Roman Catholics and settled in Chilwell Geelong,Victoria Australia