a couple of things. I think whoever said that if they gave birth in the UK the child would be British is incorrect - UK citizenship comes through your parents, not your place of birth. Even if that were the case, I think a court would consider the constitutionality of the relationship between parents and child to be inviolate. The Irish Constitution effectively considers children to be the property of their parents and in this instance, the natural fruit of marriage which cannot be given away. A child born outside of marriage is still considered differently in this instance. In practice, this has led to terrible situations where the rights of the parents to their children has almost always trumped the rights of their children to freedom from abuse (etc), even where family members have been willing (and desperate) to step in.
The other thing that's important is that adoptions aren't necessarily universal - what's recognised in one state isn't automatically recognised in another, unless there's an agreement in place. I know this because as the non-biological parent of my DD (we are a gay couple) I could adopt her in the UK (I am a UK citizen, DP is Irish, but has a right to UK citizenship, as does DD through her mother - and incidentally her father were he officially involved on a legal level), but the adoption would not be valid here in Ireland, because currently only married and single people can adopt here - not civil partners (well, as of Jan this year).
I can't think what to suggest to the OP, other than to contact the various agencies suggested and ask for good advice. An Irish family lawyer might be able to advise: Geoffrey Shannon often seems to talk good sense on the topic - Maryz knows the system inside out, and may know whether he is a good thing or not.
Is it worth seeing what the situation in Northern Ireland is?