He was a little stiff, but, I suspect it was the way the role was written. The character, Jim, had been engaged once but broke it off because he felt the girl wasn't really in love with him. It was rather a tough role to play.
Now that you've asked for more information on the film, and I am thinking about it in a different way, I see it is a bit like Far from the Madding Crowd. Both heroines are capable and intelligent, although the girl from Brooklyn, Eilis, isn't as confident or as egotistical. Both become involved with men who have struck out in love. Interestingly, both characters present their proposals more like business arrangements. They both tell the women how secure they are financially.
To be fair to Domhnall, I would have to see him in another role. I googled him and saw that he was Anna Karenina with Keira Knightley but I do not remember his character.