Registration of births in Ireland only commenced in Jan 1864, so you won't find a birth cert for Peter; however, you may a baptism record for him at this sitehttp://churchrecords.irishgenealogy.ie/churchrecords/
Where did he marry? - Ireland or elsewhere?
What was his religion?
Did he have siblings? If so, their names might help.
As far as you know, did his parents/siblings stay in Dublin?