How to Further Trace Records IN Ireland

My biggest porblem is that many of amy ancestors (grandparents) were born in Scotland but there parents were born in Ireland - unfortunately on the cencus reports that only list the country of origin and not the county in which they may hav originally lived or were born in. How do you go about finding them, especially when they have extremely common names, such as McKenna, Brannigan, Campbell, Doyle, O'Neil, Black etc.

Any and all suggestions would be greatly appreciated - thank you

Mary