The only thing I can think of that would further your case is to make a deal with your parents that YOU will be responsible for all the care, vet bills, walking, feeding, etc. Furthermore, if you fail in any of your duties toward the dog, he/she will be rehomed without any further arguments.
This was the deal I made with my parents to get my beloved Simba (Simmie). They held me to it; and, I loved Simmie enough to live up to each and every term we had decided on. Simmie was a loving, devoted companion for 17 years; and, I never regretted my decision. Neither did my parents when they saw that I was responsible enough for a dog and the joy he brought to me.
If your parents still say "No", you must abide by that. Show your maturity by accepting the "no" gracefully. Your parents are looking for maturity; and, may allow you to get a dog sometime in the future.