Thanks for your reply Cheryl and sorry for not getting back to you sooner; just begining again to to look at this branch of the family.
I can`t make any connection yet with the little information I have and this Ballinakill Connaire family. But I will keep it on file just in case.
At least Connaire is an unusual name which should make research easier. They seem to be mainly concentrated south south of Loughrea in area between Woodford, Derrybrien and Ballinakill.
My Connaires definitely originated in Laggo Moyglass. I know they were related to Larkins and Keanes in that area also.