In fact, there is some precedent for this. 黒酢, romanized kurozu, is used in sushi at a a Tokyo restaurant called Kyo-zan, which claims to be the originator of the black vinegar sushi style.
It would likely be considered a novelty in Japan, but black vinegar was super-trendy about 6-8 years ago in Japan and all sorts of new uses, including sweetened, flavored versions meant to be diluted with water as a beverage, emerged.
There is even a product called sushi kurozu, which appears to be a diluted, sweetened form of black vinegar. Since rice vinegar is slightly diluted and sweetened for the purpose of making sushi, this seems like a reasonably un-shocking, although novel, possibility.
A recipe in Japanese suggests what appears to me to be a 3:1:1 ratio of black vinegar, mirin and sugar (estimated), plus some additional salt and dried kelp. Simmering all ingredients briefly then aging for a few days in the refrigerator would be best.
There is a history of certain vinegar substitutions in sushi, sometimes for visual effect. For example, ume-zu, which is not technically a fermented vinegar but is used as a somewhat salty, pinkish alternative to vinegar made from the remnants of pickled ume apricots, can be used partially for flavor and partially for its color. I've seen a number of apple vinegar sushi recipes online (in my experience, Japan-made apple vinegar tasted slightly milder than what we call apple cider vinegar in the US). I would not say it's a completely bizarre departure from tradition to experiment with different types of vinegar. For a Japanese palate, a novel vinegar choice would probably be less surprising than, say, the presence of cream cheese.
When I go to the Korean supermarkets in LA, I usually see half an aisle just dedicated to 고추가루 in all kinds of forms (mild to spicy, fine to coarse grind) and colors. I don't know that there's any specific pepper than it is all about how sweet and mildly spicy 고추가루 is supposed to be. You could start from there to make your own by sun drying and crushing whatever peppers are available to you.
If you are looking for a substitute that you can buy at a western store, try crushed red pepper flakes (the kind you see in the shakers at pizza places). You're going to be adjusting for taste/spiciness anyway, so not much of a dealbreaker.
Best Answer
Black Vinegar is basically what it's called, and has a smoky and mellow flavor. It is made from rice, sometimes from glutinous rice and is sometimes used as a full-flavored but much cheaper balsamic vinegar. Hope this helps! :)