Shane, thanks so much for your reply!
I found the Social Security death record, as well as an Ireland civil birth record for James Kirby, but neither have his father or mother listed.
I'm going to check http://groireland.ie
as you suggested. The second website you posted a link to doesn't seem to be loading correctly so I will try accessing that page tomorrow and hope that it's fixed.
You've given me some good tips and leads on where to search next. Thanks so much for the help!