Doesn't cheerio come from the scottish gaelic word for bye? As does cheers as well I think. —This comment was unsigned.
One of the Gaelic ways of saying goodbye is indeed tìoraidh (pronounced a little like "cheery"). I can't find it in Dwelly's dictionary, which was published in 1911. I'll see if I can get a look at a newer etymological dictionary. - Donnchadh mac Alasdair.