Here’s James & Kathleen’s marriage:
Your mother’s birth is not available on-line. GRONI is the only repository for birth, death and marriage records in what is now Northern Ireland, from 1.1.1922 onwards. (Ancestry and other websites don’t have them).
Births in Northern Ireland within the past 100 years, marriages within the past 75 and deaths within the past 50 aren’t searchable on-line. They are open to the public, just not on-line. If you know all the key details eg exact date and place of birth, parents names etc, you can order a copy of a certificate from GRONI for £15. https://geni.nidirect.gov.uk
But if you don’t have all the information, you need to get in touch with them to get a search done. They will do a 5 year search for £7 and if they find a matching certificate you can purchase it for £8, coming to a total of £15. It will be posted to you a few days later. You pay over the phone using a credit card. You type your number in on the phone keypad. They don’t know what it is. They won’t deal with these searches and orders by e-mail because they need you to type the credit card number in yourself.
Phone: 0300 200 7890 (+44 300 200 7890 from outside the UK)
Mrs Martin listed at 2 Maryville St in 1924:
Also there 1932. John Martin grocer there in 1939 & 1943 & 1951 & 1960:
There’s a James A Martin burial in Roselawn. His address was 29 Maryville Ave and he died 15.9.1973. (Not sure if it’s the right family but looks roughly right).
Kathleen Martin of 2 Maryville Ave is listed as dying 17th April 1945 aged 46. She’s buried in the Glenalina extension at the City Cemetery. There’s also an Annie Maria Martin buried there who died 7th November 1919 aged 56.
Did James remarry to a Maud Elizabeth? If so she’s buried in Roselawn too. Died 19th Dec 1978 aged 71.