I have found nothing in Ireland about any of the family. It is likely that some of them also emigrated. The deaths of Michael and Bridget are not yet available to view so it is not possible to tie them down at this stage. Hopefully when there is a future update you will be able to determine when they died. They do not appear in the census of 1901 so it is likely they died sometime between the birth of their last child and that date.
However I did find a few leads for you regarding their other children.
Patrick died in New York in 1927. He was widowed at the time of his death. I have not yet found a marriage for him but I will look again later. I found his death on Family Search and it names his parents as Michael and Bridget Cooney. His date of birth is slightly out but this is very common for that time. His occupation at time of death is listed as Gardener.
But I also found a passport application for Patrick dated 1922 on Ancestry and it has his photo on it which is always a bonus. His place of birth is wrongly transcribed as Bally Mc Annele. Do you have an Ancestry account? The passport application has details of his arrival in the US and it states that he is intending to visit Ireland so he obviously had family still in Ireland in 1922.
Catherine also died in New York. She is listed as Katheryn, single. She died in 1943.
I'll try to find some more information for you.