Nope, the Romans coined it referring to the jibberish that the Romans heard when the Germanic tribes spoke, “bar, bar, bar, bar.”
Homer doesn't have the word barbaros but he does have barbarophonos, "speaking a foreign language," applied to the Carians, in Iliad 2.867. The earliest authors to have the word barbaros are the philosopher Heraclitus and the poet Aeschylus (in his play The Persians dated to 472 B.C.).
Herodotus mentions the Garamantes briefly a couple of times in his account of Libya:
4.174-175: Further inland, to the south of this region, in the part of Libya that is teeming with wild animals, are the Garamantes, who shun all human intercourse and contact. They have no weapons of war and no knowledge of ways to defend themselves. The Garamantes are the neighbors of the Nasamontes inland...
4.183-184: Another ten days' journey after Augila there is a third hill of salt, with water and a great many fruit-bearing palm-trees...A very large tribe called the Garamantes lives here. They put a layer of soil on top of the salt and so have land to cultivate...The Garamantes use four-horse chariots to hunt the cave-dwelling Ethiopians, because the cave-dwelling Ethiopians are the fastest people of any of whom we have been brought a report....Another ten days' journey further on from the Garamantes is another hill and water, again with people living in the vicinity. This is a tribe called the Atrarantes...
(Translation by Robin Waterfield, in the Oxford World's Classics edition.)
Then why weren't they called bierbarians?