The word more commonly used is "triune." "Triunate" adds a redundant adjective ending and is not in common usage, so you are not going to find it in a dictionary. Dictionaries record the English language, not the other way around. For follow-up questions, or other similar ones, you'll find the better place is the Q & A thread at /r/linguistics.

Sorry, but this is not the appropriate subreddit for this question. Possibly /r/linguistics, or perhaps /r/Christianity.