Birth records for people born less than 100 years ago in Northern Ireland aren’t on-line. You would need to contact GRONI in Belfast to ask them to search.
PRONI (the public record office) in Belfast have this probate file, which relates to a Heslop family from Co Durham with assets in Northern Ireland. I wonder if it’s connected to your family?
Heslop Thomas Paul of 29 Stephenson Terrace Felling county Durham died 18 January 1935 Probate Durham 14 March to Mary Heslop the widow Robert Heslop printer and William Hope railway company's checker. Effects in Northern Ireland £45. Re-sealed Belfast 11 June.