This might be an arbitrary question, but how often often does one see a word in Irish that has two consecutive long vowels? I'm reasonably sure that tríú is the first example I've seen in this course. Does that word happen to be an oddity or is it merely a reflection of my limited vocabulary?
Most of the examples that I can think of are essentially compund words, so you need two thing to come together, a word than ends in a fada, and a suffix that starts with one. In the case of the ú suffix indicating numercial order, you get dóú, tríú, and séú, because a lot of numbers (relatively speaking) end in a fada.
In most other categories of words, the proportion of words than end in a fada is much lower than 30%, and not all of them can take a suffix, so consecutive fadas are scarce, but not that unusual. In the case of the diminutive endings ín and óg, you have examples like bóín or buíóg, but there are probably more words ending in í than in ó. Another suffix that starts with a fada is the adjectival úil, giving rise to examples like croíúil.
You could probably throw a regex against teanglann.ie and get a fairly comprehensive list easily enough.