Try to persuade who? Your mom? Oh, that is a hard one trying to persuade the mom. (if that is the case) How old are you? I guess if you are trying to persuade the mom, you just need to show her you have a good sense of responsibility and prove to her that you are willing to be responsible and be the one who takes care of the dog. A dog is a lot of work. Besides feeding and watering, you need to be sure to exercise it, bathe it, give it attention. Mine wants attention constantly so attention is a lifelong (the dog's) commitment not just an hour a day thing. Renee made a good suggestion to get a dog that is out of puppy stage b/c puppies are a LOT more work than a dog who has already been potty trained. Plus puppies can tend to chew - - a lot. Your socks, your shoes, your title to your car, any papers left within reach (which my dog is so big now it is at about 5 feet (his reach)), your pillows, your wood around the frame of your doorway outside, the top of his igloo doghouse, the vinyl on the actual house we live in, the drain pipes for the rain, the knobs to turn on the grill, etc. etc. I am just trying to give you a good idea of what they can destroy b/c you can think all day of how you will keep stuff put up so they can't get it and chew on it, and they will think to chew on the one thing you never thought of. What I am saying is that just be ready for this and prove to your mom that this is what you want and you are willing to take the responsibility. These things are going to happen no matter how much you are prepared so it really falls to how willing you are to deal with it.
I hope that it works out for you, I just wanted you to know how much time and effort it takes to have a dog. There are so many people in my neighborhood who have dogs and don't walk them or leave them tied in their garage and you just have to be ready to have one so that does not happen to them. Good Luck!