Coleman Green's father was Patrick Green. Bridget Burke's parents were Thomas Burke & Bridget Conneely.
You were correct in thinking their son Patrick came to the US. He married Catherine Conroy from Cuilleen, Carna in South Boston on 02 Dec 1917.
Not sure if you know this or not, but your grandmother Margaret (Jennings) Green was from Letterard, Carna.
Hope this helps.
Portsmouth, Rhode Island