I have some research on the BYARD family.
My grandfather was Welsh (his father moved across the english/welsh border looking for work. I have traced my family back top 1798 in England (where I live).
I have never heard of any Irish Byards (the name certainly isn't Irish, I believe it's origins are french - Bayard).
There appears to be two or three main areas for the Byards in England : Derbyshire,Gloucestershire, and South Wales.