Marriages in Northern Ireland within the past 75 years are not on-line. So, as I write today, those after 7th December 1942 are not on the GRONI website. (They are added on a day by day basis as the calendar advances). Births within the past 100 years won’t be on the site either. So you have to go to PRONI or GRONI in person to view these records. Or, if you can’t do that, contact GRONI by phone or e-mail (but there may be a search fee).
If George died in Northern Ireland in 2008, you could also search for a probate file for him. If he left a will it might name any children he left bequests to. I searched the England & Wales Probate site but he doesn't appear to be listed there, so perhaps he left a will probated in NI.
I think that probate files for 2008 and later years are still held by the Probate Court in Belfast, though the on-line information about this is most confusing. One website seems to suggest that probate files up to 2010 are with PRONI. (If so, you can view them there free, but only if you go in person). Another suggests that files for 2008/9 are still with the Probate Court. Frankly I don’t know. I suggest you contact the Probate Court to check. The bad news is that if the files are still there, they may want a search fee which looks to be £22. But you’ll need to check that with them.
https://www.justice-ni.gov.uk/articles/probate