I'm afraid I can't help you with Maynooth, though I have a lot of cemetery records and photos of the majority of graves in Celbridge (for which there are records headstones existing). I have checked these for the surname of Coffey and afraid I did not find it.
Maynooth, as I remember it, is a much smaller graveyard, so should be far easier to make your way around it. However, depending on Teresa's circumstances, it's very possible there is no headstone to find at all, in which case, you need to find burial records. When I was trying to find these for Celbridge, I was passed back and forth from the local parish priest to the unhelpful person responsible who held the records and caretaking duties of the graveyard. I ended up contacting Kildare Co. Council, who at first referred me back to the priest and the caretaker (it is so frustrating). But then my father approached our local helpful politician, who contacted the Co. Council, and voila! I had an instant email with the old records which had been scanned in! So, I recommend you try one or all of these things, though I realise it's not so easy when you're not in Ireland.