How can I convince my step dad to get a dog?

"I kept begging my mom to let me have a dog."

Constantly begging is not only childish, but annoying. You're not doing yourself any favors by acting like a brat.

"She likes dogs but she thinks I might not clean after it, but obviously I will."

Obviously you won't. You're not different from any other teen we get on these boards. They might last a week or even two before realizing how much WORK a dog is, then they find all sorts of excuses not to live up to their promises and expect mom to take over.

She says the only way I can get a dog is if her boyfriend (my step dad) allows me too. He likes some dogs, but he doesn't really like them in the house."

You don't "convince" him of anything. You ask him. His house, his rules. However, if he won't allow the dog in the house, it is CRUEL and SELFISH to throw a dog out in the yard like some lawn ornament, so you shouldn't get one.

Move out, get a job, get yoru own place. Can't? Tough.

Bribing, whining, begging and acting like a toddler is not only very immature, it shows you wont be responsible enough to take care of a dog

Your mom knows you wont clean up after it and wont take care of it. Your step father has also told you no. That means NO.

Just keep asking, bring up what a good breed yorkies are. I was in the same situation as you, my step dad hated animals. I ended up buying a yorkie puppy and just bringing it home, he wasn't happy about it but a couple days later to my surprise he fell in love with the puppy. No one can resist a yorkies adorable face. I say go for & just try to show him different.

bribe him. import some sexy and racy photos in his phone and then tell threaten to show your mom the pics unless he gets a dog.