Tell him U would really like to get a lizard, or anoconda, or pit bull- but U would be willing to settle for something like a ferret, or a rat or maybe-dang it- even a stupid hamster! I think U may end up with a hamster!
show your interest on it. go to the pet shop and have a nice conversation. slowly and not too demanding. and you should convince your father that you can take care of it with the best care ever. tell him your desire with whole hearted. good luck^^
Spend a week picking up after yourself and keeping your room neat. Then ask again, promising to clean the cage every day. If he says yes, keep that promise. If you don't, he may get rid of it. If he says yes, stay calm. Look a little disappointed but don't get mad or start crying. Tantrums will leave him with an even worse attitude about you having a hamster. Keep up the neatness, and ask again in about a week.
I wish I could tell you I have been wanting one for over three years now and I've pretty much tried anything. I had a guinea pig (never wanted it my sister did) and she got bored with them in like a week that's why my father says no... If something works for you tell me what you did please! But I do like DeepDark's and leeyana's answer.