GRONI is the only repository for birth, death and marriage records in what is now Northern Ireland, from 1.1.1922 onwards. (As others have explained, Ancestry and other websites dont have them).
Births in Northern Ireland within the past 100 years, marriages within the past 75 and deaths within the past 50 arent 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 (sterling).
https://geni.nidirect.gov.ukBut if you dont 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 dont know what it is. They wont deal with these searches and orders by e-mail or post because they need you to type the credit card number in yourself.
The numbers I have used are 0300 200 7890 (+44 300 200 7890 from outside the UK)
Alternatively if you live near Belfast, you can go in person to either GRONI or PRONI (both in Belfast). They are the only places where you can search recent records, right up to those registered yesterday. You can view each cert there for £2.50, and if you want a certified copy its an extra £8. (Posted out in 2 to 3 weeks time).