Hi
You have definitely been on the right track in search of William Connon's descendants, including myself. There are 29 currently living, scattered about USA, Ireland, Canada, Argentina and Spain.
HOWEVER, William himself abandoned his wife Isabella and the 4 children at some time before the year 1908. They never saw him again, and moved, without him, to Argentina. It is believed he went to live first in Canada and then the USA where he apparently settled in the area of Chicago. So quite probably there are more of his descendants via that connection.
Another bit of gossip is that William married 15-yr-old Isabella in 1894, six weeks before the birth of their first son.