If you'll provide more details about the Doonan family, some of us might be able to help you more.
Did James Doonan emigrate to Canada, the U.S., Australia, England... or remain in Ireland? Who and when did he marry, and what were his children's names? Do you know his occupation (perhaps from censuses, if no other sources)? Where did he live, when did he die, and where is he buried?