No, there are neither theoretic nor practical evidence show toothpaste can reduce black eyes. In fact, millions of failures have proved that toothpaste doesn't help black eyes or spots.
If you want to get rid of your black eyes, you should:
1. Apply ice compress to the eye as soon as it is punched. Once bruise is done, nearly nothing can be done to help.
2. When the bruise is done, you can also apply ice pack to reduce swelling.
You'd better not use the toothpaste to reduce your black eyes which will stimulate the eyes skin around your eyes. You should use something mild to treat your black eyes. First of all, you need to prepare the sunglasses when you are out. That is very important which will protect your eyes from the uv rays and other bad lights. Then you could have the good rest for the eyes. Next you could use the warm compress by finding the clean cloth and hot water to make your eyes feel comfortable. Your black eyes will be reduced soon.