Most often I found that babies were buried back with other family members so, if not done already, could go back to where your grandfather or grandmother's parents were buried if they died before the baby . Families made the trip back to the townlands to these family burial areas. Once in a while, was lucky to find a death notice in one of the two Belfast newspapers at the Central Library which gave the burying ground (or area) where burial was occurred. Best wishes with your search.