William John Breen married Lucinda Parker 3.12.1862 at St Ann’s Church of Ireland, Belfast.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1862/09624/5490329.pdf
Birth of son William John Breen 27.3.1865 Belfast at 23 Verner St, Belfast.
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1865/03576/2318055.pdf
Birth registration only started on 1.1.1864 so if a child was born in 1863 there won’t be a birth certificate. There is a baptism for a James Breen in 1863 on the rootsireland site (subscription). A number of trees on Ancestry have his date of birth as November 1864 but that can’t be correct as it’s only 5 months before William’s birth in March 1865.