Siobhan,
If your timescale of 1910 – 1915 is accurate and if Richard was born in Belfast, then there are only 2 births that fit that information:
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1911/01542/1624491.pdf
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1912/01475/1601003.pdf
Here’s the two families in the 1911 census:
http://www.census.nationalarchives.ie/pages/1911/Antrim/Cromac/University_Avenue/167513/
http://www.census.nationalarchives.ie/pages/1911/Antrim/Shankill/Legane_Street/172003/
Legane St is in the Shankill whereas University Ave is about a mile away. But people can move of course.
You say that Richard Wilson was married by 1934. I searched from 1926 – 1934 and found 2 Richard Wilson marriages in Belfast. One on 8.8.1927 to Josephine Lettice and the other on 3.10.1934 to Martha Graham. You’ll have to pay to view those years, but hopefully the fathers names, the fathers’ occupations and the address will indicate which, if either, might be the family you are looking for. You can view the original certificates on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
This site doesn’t assist with tracing living people (for privacy reasons). Identifying the correct Richard who, by his likely age, must be long deceased is completely understandable but I would caution against trying to contact any living descendants, especially where illegitimacy may be involved, as that can cause considerable distress.
