I think it's a pretty safe assumption that the Dal Riadans had them earlier than 500 AD and didn't start using them after the rest of the world quit doing so. I think it's also a pretty safe assumption that if one Irish kingdom/people used chariots for warfare, that others did as well. Especially when Irish texts tell us they did so. The surviving written texts of the Tain may have been written down in the 12th century, but scholars and achaeologists almost universally agree that they were originally part of the much older Irish Oral tradition.
Now I did use the word assumption, however, it is a logical assumption using the info we have. That's what a lot of current "History" is, logical assumptions based on relevant information available.
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