Help with convincing...?

He's an adorable dog. Have your parents expressed an opinion on getting a dog just yet? That might change things. Usually when they say no, the answer is firm and there's no moving them, even with browbeating which could also just get you into trouble. Just flat out ask them. Tell them that you want to adopt a dog to save his life, you're lonely without your guinea pig but want something with more personality, something that can be your best friend. Show them the dog, tell them what you will pay for, what you will do for the dog (to be sure they're not taking on the responsibility), etc.