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''
In Irish it's "laethanta sona"
'Of the day' is an Lae in the Irish language.It's an Latha in (Scottish) Gaelic.
In Irish Gaelic as a greeting, Dia dhuit! On taking leave Lá maith agat!In the sense of 'a good day' it's Lá maith.In Scots Gaelic latha math or latha bréagha.
Irish (Gaelic): lá Scottish Gaelic: lathaLá, pronounced like law.
In Irish, 'the common good' would be 'leas an phobail'.In Scottish Gaelic: ?
maithmaith
The Irish Gaelic for "Happy St. Brigid's Day" is "Lá Fhéile Bríde sona duit." This phrase conveys good wishes for the celebration of St. Brigid, who is one of Ireland's patron saints. The day is celebrated on February 1st, marking the beginning of spring in the Irish calendar.
In Irish Gaelic: slán leat (slán libh. plural)
In Irish: leasdeirfiúr. In Scottish Gaelic: leas-phiuthar
go mhaith
In Irish it's "bia maith, sláinte mhaith"
irish: focal an lae