Limerick can refer to the city or the county and it will be difficult to find such early Irish records without more details. Many records for that period do not survive and of thise that do not all will be found online. In addition to all that, if tyou were to find a John Hayes with brother Cornelius it still wouldn't prove you've found the right family.
Does John's marriage list a father's name & occupation?
Where did you get Cornelius' name from?