Okay, so according to parish records, Bernard was born to Hugh and Anne/Ann , 28 Jul 1844.
Hugh and Anne/Ann (nee Galbraith/Gilbraith) were married in the Glenarm Roman Catholic chapel in April 1828.
From Hugh's death registration (d. 22 March 1866 aged 61) we can derive a birthdate for Hugh of about 1805. Unfortunately I did not come across any parish records to confirm this birth date. As we go further back, fewer and fewer records survive.