Have a good day in Irish Gaelic?

To answer the question, "Have a nice day" is not something most Irish people would say in Irish Gaelic. That's an American phrase. A phrase like ádh mór! (= good luck - used mostly in Ulster Irish) and maybe tóg(a'í) go réidh é! (= take it easy - used quite often in Connemara) might be what Irish-speaking people would say in such circumstances. Or you could try "Tá súil agam go mbeidh lá breá agat" which means

"I'm hoping you will have a fine day''