I had a look at Patrick Carroll births from 1864 to 1874 when I was at the NI Registry Office for you. The only one with a father called james was 23 Oct 1873 at Ennislare. Father was James Carroll (a farmer) and the mother was Catherine, nee McKenna.
A quick search of other births showed 3 siblings - Mary Jane born 29 Sep 1868, Sarah born 12 Jan 1871 & Patrick born 23 Oct 1873. All were registered in Armagh district.
Hopefully that gives you enough to see if it fits in with what you have.
Best of Luck