We're related - very distantly! I'm a descendant of Matthew Tierney (b 1826); my mother was a Tierney before becoming a Pearson.
I spent a long time about a dozen years ago researching the Tierneys. I traced them back through the censuses, and then made use of the Roman Catholic records for St Mary Moorfields church, which holds baptism records for my Matthew in 1826 (who incidentally was also a Cooper by profession), and a John born in 1829 (though I see you and others have him born 1833, so perhaps the original John died and another replaced him then?). They listed the mother as Jane, nee Hicks (Johanna she's listed as, the records being in Latin), and also recorded Matthew's death in 1836, aged 54, which I think you know about.
You've gone one better than me though, and actually found out where in Ireland they came from - that's excellent detective work!
That's all I know about them going backwards (though I know a lot about them going forwards!). I would love to hear any other info you might have on them.