Doubt its vinyl, its likely EPDM rubber or some other compound of rubber. First I would determine exactly what material it is.
Eternabond tape is great, but it only covers the tear. If you have a EPDM rubber roof, I would encourage you to research a product called "liquid roof". This is a liquid rubber (like a thick paint) that you brush on to your roof. It is the same chemical compound as your existing roof and adheres to the original roof and creates a seamless repair. I used this to fix a hole in my roof years ago. Cost about $60 for a quart (I think) and took about an hour to prep, mix, paint of and clean up. It is a one piece roof membrane again.
Good luck, make sure to keep it dry before you fix it. Make sure to clean the section very well before you fix it. The cleaner it is, the better and longer lasting your fix will be.