"I am living in west Cork."
Translation:Tá cónaí orm i gCorcaigh thiar.
Several books teach "tá cónaí orm", one such book is Colloquial Irish. To learn to speak Irish you're going to need much more material than Duolingo. No knock on Duolingo, but it will only get you so far. I think the reason they don't accept "Tá mé i mo chonaí" is for this reason, to force you to learn another way of expressing it.
I have no previous knowledge in Irish, I only know what Duolingo has taught me earlier and I have learned "I am living" is either "Táim i mo cónaí" or "Tá mé i mo cónaí". This optional way of expressing "living" hasn't been presented before and it is a complete guessing game for me to try to get it right.
Duolingo is designed to teach Irish, and, like just about every teaching resource out there, it focuses on teaching a single version of Irish. Duolingo teaches an Caighdeán.
Duolingo wasn't created to test your existing Irish, but a huge amount of work was done to add lots of regional variations as acceptable answers, to avoid discouraging people like you, at the expense of doing more work to add additional new content to the course. But the contributors rely on requests from speakers of particular dialects to notify them of particular variations, and not all possible variants have been added.