I can understand how badly you want this done, hun - I had the same thing with my lip. My mom was really against it. It's important not to try and guilt trip your dad, because he will most likely (and rightly) see that as immature, and the more immature you look, the less he will think you are mature enough to get this piercing. I agree with what is said above, look up pros and cons, let him know why you want this done, i.e. not because anyone else has it, etc, let him know that you plan on getting a small stud and not a massive nose ring - it might make all the difference. Whatever you end up saying, make sure you present it calmly and rationally and not in a temper or anything. When it comes to this, you need to be as mature as possible when talking about it, know your facts, persuade gently. It worked for me :)
Also, DO NOT attempt to do it yourself at home (or elsewhere) - there are too many risks - and any piercing artist worth his/her salt will not pierce you without parental consent if it is required in your area. If they are willing, it is probably not a good idea to get it done there.
Hope this helps :)