Civil registration of births started in Ireland in 1864, and for dates before this time you are dependant on church records - i.e. baptisms. To search for possible records you need to know the denomination of your ancestor and also which town or parish they lived. Very few parishes have records back as far as the 1700s, and RC records before 1830, particularly for rural areas, would be quite rare.
It's also worth mentioning that Kelly was the second most common surname in Ireland (after Murphy) which will make it difficult to trace the correct family unless you have more clues - such as name of parents, siblings, townland or other clues.
see :
Introduction to Irish Records My Ancestor came from Ireland - where do I start? Shane
