You SHOULD be able to order "transcriptions" (i.e. uncertified, but containing all the info on a ""real" birth certificate) from GRONI for £6 with the following details:
Name, District, Year (& Quarter if after 1878), Volume and Page.
These can be obtained from the LDS website but it seems to confuse the issue if you tell GRONI staff that's where you got them!
I know someone who ordered a couple last week and he was initially told you couldn't order using the LDS information. Then he gave them the above references (which he got from LDS) and they sent him the transcripts.

By the way, if you can get to Belfast the GRONI office in Chichester St allows you to get the information in person for £3 per entry, but you do have to book a couple of weeks in advance as space is very limited. Once you're there though, the post 1922 indexes (and earlier marriage index) are excellent and very easily searched. For pre 1922 births and deaths, check out the references on LDS pilot site before you go.