I just did a quick search on ancestry.com for Iwery. So many different versions of the phonetic pronunciation! Iwery, Iorry, Irey, Iorway, Iry, Irohey.

I fear this requires widening my search. And it looks so simple a name with only 5 characters!
Avery is popular for England but when I search for Ireland it produces a lot of Lavery's.