How do I convince my mom to let us get a dog?

Okay, so me and my brother really want a dog!! weve been wanting one forever. my dad wants one too. a few years ago he promised us that we would get a dog in the spring but never did. my mom is the one thats keeping us from getting a dog, she said that when everyone is at school and work it will destroy the house and no one will take care of it. i actually would take care of it i love dogs and all animals, i have been searching the local dog shelters and have found some really great dogs, that are already house broken. my birthday is next month, and I am willing to pay for the dog and his/her supplies myself with my own money. We have 4 cats, but cats are such a boring pet. I do love my cats but i do want a dog, we have a huge backyard, with plenty of places for him to run, and we could probably get a dog that won't bark alot, so how can I convince my mom to let us have one?? Please help!!!!