A report in the Egyptian paper Al-Ahram, translated by MEMRI, claims that coins have been found from the time of Joseph, which bear his image:
"The researchers discovered the coins when they sifted through thousands of small archeological artifacts stored in [the vaults of] the Museum of Egypt. [Initially] they took them for charms, but a thorough examination revealed that the coins bore the year in which they were minted and their value, or effigies of the pharaohs [who ruled] at the time of their minting. Some of the coins are from the time when Joseph lived in Egypt, and bear his name and portrait...
"The researcher identified coins from many different periods, including coins that bore special markings identifying them as being from the era of Joseph. Among these, there was one coin that had an inscription on it, and an image of a cow symbolizing Pharaoh's dream about the seven fat cows and seven lean cows, and the seven green stalks of grain and seven dry stalks of grain. It was found that the inscriptions of this early period were usually simple, since writing was still in its early stages, and consequently there was difficulty in deciphering the writing on these coins. But the research team [managed to] translate [the writing on the coin] by comparing it to the earliest known hieroglyphic texts…
"Joseph's name appears twice on this coin, written in hieroglyphs: once the original name, Joseph, and once his Egyptian name, Saba Sabani, which was given to him by Pharaoh when he became treasurer. There is also an image of Joseph, who was part of the Egyptian administration at the time.
The debate in this case seems to revolve around whether these are really coins or not. Either way, it does seem extremly unlikely that these really are authentic pictures of Joseph. There is no other archaeological proof of Joseph's existence and a coin/amulet apparently confirming the biblical story seems particularly convenient.
But if only. I would love to see the picture of the man the Bible called "well-built and good-looking".