Conway Family - Limerick

Hello! Thank you so much for having me in your group.

I have a particularly tricky situation that I am hoping to gain some help with. I have a Conway to Conway coupling. What I know is as follows (I do have an ancestry tree Conway and Thomas):
1. James M Conway (born around 1850) moved to America in 1868 and a few years in, met Catherine Conway (born around 1850) who had moved to America in 1872. They fell in love but had to return to Ireland. 
2. 17FEB1877, their first child, Martin Conway, was born in Ireland, registered in Rathskeale No. 1, Limerick to James Conway and Catherine Conway Conway and the place of Father's residence is listed as REENS - I have this birth certificate attached. 
3. FEB1879, they are back on American soil, and my great grandfather John Joseph Conway is born in NYC. The story told in my family is "He was almost born on the boat".
4. The 1880 American Census, they are all living in NYC together at 88 Horatio Street, NYC. Father's birth Ireland, Mother's birth Ireland, Martin's birth Ireland, John's birth NYC.
5. James M Conway opened a bar in NY in his later years. His son, my great grandfather said his "grandfather had a pub in Limerick" - but again I struggle with which Conway grandparent of his he meant because I am unsure if the Limerick connection is for James or Catherine?

I need some direction around a few things and was hoping the group's collective wisdom may be able to help. 

1. Any ideas on why they would have chosen Reens, except if family was in the area? It doesn't look like a heavily populated area and I don't see any time in history where it was a capital/major city. Also, this could be James OR Catherine's family (so many options!) but was there tradition that stated that one of their families would have priority? 
2. Am I right in assuming that Martin may have been the M in James M or that James or Catherine's father was a Martin?
3. What would you suggest be my next vein of research or step to help narrow this down?

Thank you so kindly. I greatly appreciate your time in having read such a long post and any thoughts you may have on how to best solve this wall for me.

Thank you kindly.