Well, generally speaking, you are not supposed to go tanning with a black eye. As we know that when blood and other fluids collect in the space around the eye, a black eye can occur. And if you go tanning, it can make your symptom worse. So you should leave the tanning for a couple of days until swelling goes down. To speed up the recovery, you can put ice packs on the swelling. And then, butter on the bruising will be good too. By the way, warm compress will also be effective for your black eyes, for they can make your blood flow smoothly. So you can just put a warm cloth on your eyes. anyway, just wait for a few days until the symptom disappear.