Apparently from or at least influenced by Middle Englishtyde, though the vowel is unexpected. The word is attested from the 17th century if not earlier, when it would have been pronounced /ˈt̪ˠɯːdʲə/; an Irish form *tíde with /iː/ would be expected in a straightforward borrowing from Middle English (and does occur in Scottish Gaelictìde). The relationship between this form and the forms taoille and traoille is also unclear. None of the forms has an entry in the Dictionary of the Irish Language; the Historical Irish Corpus shows taoide being attested from the early 17th century but taoille not until the early 19th century, and traoille is not found in the corpus at all.
