Your profile doesn't tell me how old you are, so I'll ask. How old are you? Are you working?
My advice is to convince them to get a small one (Cats work great for this, but some dogs are perfect too) and that you'll be 100% responsible for it. Feed it, clean up after it, etc. This works better in your favour if you can pay for the food, medical bills, etc for the animal.
I personally can't imagine life without a dog, so I hope you manage to convince your parents to let you have one... or at least a cat.
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