Many thanks go to both Elwyn and aghadowey for your advice and help in this matter. Unfortunately, GRONI in Belfast, have confirmed that my Grandmother Margaret, was never registered for a birth certificate.

Your assistance was and is greatly appreciated.
All is not lost though! I have made a member connection on A*******y UK, who has directed me to my Great Grandfather's WW1 service record. Contained inside are details of his children's birthdates. At that moment in time, he had three daughters only. My Grandmother was the eldest child. I now know her birthday. Yay!!
Thanks also go to Miss Poohs for trying to get some help, advice and information that would have helped us to obtain Margaret's birth certificate had it existed.