Several ancient accounts come to mind!
The Book of Kings in the Hebrew Bible relates how Jezebel, a ninth-century Phoenician princess and the widow of King Ahab of Israel, painted her eyes with antimony (as an eyeliner, it seems) and arranged her hair on the eve of her violent death at the hands of King Jehu of Israel ((2 Kgs 9:30). Although later Judahite prophets associated eye cosmetics with prostitution (Jer. 4:30; Ezek. 23:40), in this context the reader should probably understand Jezebel as desiring to make herself presentable for her final public appearance.
Herodotus, in his description of the Persian forces under Xerxes, notes that the Phoenician contingents "had on their heads helmets very close in style to those of the Greeks, and having put on linen breastplates, they had rimless shields and javelins" (7.89.1). This supports the overall impression from other evidence that Phoenicians used similar arms and armaments as the Greeks.
Elsewhere, Herodotus claims that the Phoenicians normally circumcised their children but that those in contact with the Greek world did not maintain the practice (2.104.3-4).
According to Polybius, the Sicilian historian Timaeus of Tauromenium placed a speech in the mouth of Timeoleon in which he mocked the Carthaginians for their use of underwear, among other things: "they wear undergarments beneath their tunics, so that not even when they die in battle do they become exposed to their enemies" (12.26a.4 = Timaios BNJ 566 F 31b).
Plautus's play Poenulus (The Little Carthaginian) depicts the Carthaginian merchant Hanno as wearing earrings (981) as well as a "long tunic, as if an innkeeper's boy/slave" (1298). Romans audiences would have considered these signs of effeminacy, and the comments from the other characters seem derogatory and vaguely anti-Semitic, but Hanno actually emerges as the sympathetic protagonist of the story.
Whether any of these details are reliable remains difficult to say, but I'm inclined to believe that they reflect some degree of reality. And I'll add more sources here if anything else pops up in my memory. :)