Allyson is not an Irish word and has no meaning in Irish.
Allyson/Allison, comes from the German name, meaning "Of noble birth".
Allyson Good's birth name is Allyson Sands.
Allyson Everitt's birth name is Allyson J. Edward.
Allyson Felix's birth name is Allyson Michelle Felix.
Allyson Downey's birth name is Allyson Lee Downey.
Allyson Lupovich's birth name is Allyson Sadie Lupovich.
Allyson Ames's birth name is Jacqueline Allyson Schwab.
Allyson Fwlix's brothers name is Wes Felix
June Allyson's birth name is Eleanor Geisman.
It has no meaning in Irish; it's not an Irish Gaelic name.
It's not an Irish name so it has no meaning in Irish.
It doesn't mean anything in Irish: it's not an Irish name. I believe it's French.