To find non-white Jesus, you need to look to churches and peoples that were Christians before Europeans were, or at least before Western European artistic styles began creeping into everything. When you do that, you find depictions of Christ that are African, Asiatic, etc. To the extent that you find other things than these native styles, the fleshy, Western-styled art is what is non-traditional to these places.
Here are a few examples:
Depiction of the last supper from the Armenian-language Matenadaran gospel, 1287 AD
(This seems to be something of an Oriental peculiarity, as the Syriac Orthodox also have ancient images depicting the last supper where the table is round, as opposed to the more standard flat, long shot as found in, e.g., Michaelangelo's Last Supper.)
Image of Christ (center), St. Thomas (L), and Simon Peter (R), from an 18th century illustrated gospel in Alqosh, Iraq
Christ Pantocrator (12th century), Monastery of St. Anthony on the Red Sea, Egypt
Ethiopian triptych icon (15th century), known by the monks of the monastery of St. Stephen where it is located as the icon of "He who listens"
These are the traditional iconographic forms of these peoples who were among the first to convert to Christianity during the apostolic age, and hence they form an invaluable treasure for all Christians who wish to know how the ancients saw Christ, and to worship Him as they did. To me it has nothing to do with 'representation' in some kind of modern, western political sense, but rather the plain fact that the one Christ is the Christ of the Armenians, of the Syriacs/Assyrians, of the Egyptians, of the Ethiopians, and all others just as much as He is the Christ of the northern and southern European painters who established the Western standards of how Christ is depicted in western churches like the Roman Catholic Church or the various Protestant traditions (those of them that make use of images in worship, that is). Because He is the God of all the world and all of its peoples, of course you can find these different styles, and probably even more that might not have such a long history, but I suppose still prove that the inculturation of the Gospel of life continues in our own day among the more recently Christianized, as well. And praise be to God for that!
