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 (sterling). 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 or post because they need you to type the credit card number in yourself.
Phone: 0300 200 7890 (+44 300 200 7890 from outside the UK)
A Hugh Rogers married an Elizabeth Kearney on 30.4.1940 in Newry & Mourne district (which includes Kilkeel). You can view that certificate on the GRONI site for £2.50.