According to the Old Irish Naming System, the first born son is named after the husband's father, so you would be looking for a William Mahoney as the father of Timothy Mahoney.The second born son is named after the wife's father, but I did not see a second born son.
In the Old Irish Naming System, the first born daughter is named after the mother's mother, so the mother of Bridget Kilkeary would be a Catherine or Kate Kilkeary nee ????.The second born daughter is named after the husband's mother, so the mother of Timothy Mahoney would be either a Margaret or Julia Mahoney nee ????.It is difficult to tell because they appear to be twins.
I wonder if it would go by which one was born first.