Most Helpful Guy
Whenever I wanted something bad enough, I'd write a paper and make a powerpoint presentation on it. The fact I put enough effort into would make them give in and listen. *True Story*
However, I doubt you want to do these things, so I suggest simply making an argument for your case. Ask them what they're concerns are and answer with reasonable rebuttals. Make sure you emphasize that you'll take care of the dog so they don't need to worry, and also make sure you are very calm when talking to your parents. Anger makes parents get more stubborn and say no.
If they are worried about the dog's upkeep money, you are going to need to try and find a source of income, whether that is doing chores for money or babysitting or whatever.
The key point you need to emphasize is that the dog will only bring positive things to their life while you will take care of all the negative things (upkeep, training the dog, feeding him etc.)0