Kinsella says in his notes to 'The Tain' that the tale of Deirdre and the Sons of Usneth (or two other spellings) is from the 8th or 9th century, but didn't say how old the manuscript was that he translated. Many Welsh and Irish manuscripts are to a large extent copied from older ones that have disappeared, so it's hard to know how old the basic story is, or how much it was revised in the known later manuscripts. Also one sometimes has small pieces of a tale in an old manuscript, but the only complete version in a much later one. 'The Tain' was supposed to have taken place about the time of Chirst's birth, but not every thing fits with this. Fergus is of considerable importance is the tale of Deirdre, and the real Fergus can be put at about c 560 C.E. (my rough estimate). One tale of the Mabinogion has him in King Arthur's time, which is about 50 years too early (but the Welsh tales, and King Arthur stories put several historical figures too early, e.g., Peredur of York = Percival/Parsifall, Owain son of Urien).

Actually, what is perhaps the earliest Welsh song is one by Taliesin in 'The Tale of Taliesin', which one editor puts in the 'Mabinogi' (Patrick K. Ford), and some don't (there are also poems purportedly by Taliesin there, too, but one is specifically called a song). The setting for this is in the reign of the real Maelgwyn/Maglocunus, c 520-551 C.E. (when Maelgwyn died of bubonic plague). The oldest manuscript is of the mid-16th century.