Keep in mind, where James Cecil Kearney was born in December, he may have been registered in the next quarter (Jan-Mar 1887), which adds several more possibilities. Coincidentally, there was a James registered in Co. Armagh for that quarter. (There's also one in Dublin-South, Kells, Omagh, Ballycastle, & Navan).
I usually recommend to look for his marriage & death record to see if his mother's name is listed. If you could find out that, it would be a good start. The records possibly could list where he was from as well.