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.
Irish (Gaelic): lá Scottish Gaelic: lathaLá, pronounced like law.
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.
In Irish, 'the common good' would be 'leas an phobail'.In Scottish Gaelic: ?
maithmaith
In Irish Gaelic: slán leat (slán libh. plural)
go mhaith
In Irish: leasdeirfiúr. In Scottish Gaelic: leas-phiuthar
irish: focal an lae
In Irish it's "bia maith, sláinte mhaith"
Irish Gaelic: míorúilt; éacht; iontas. Scots Gaelic: ?