first of all, how old are you, if you are under 18 (assuming you are in the states, and if you are considered a "Minor" where you live) then you are just outta luck.
try to get them somewhere where you can handle snakes and show them that they don't instintively try to kill you.
Hate to tell you this, but if it has a mouth, it CAN and POSSIBLY WILL bite. So NEVER say the snake won't bite, because the next thing you know your mother is running around with a bp latched onto her arm. lol
Do RESEARCH. Show your parents that you are putting effort into this. Do chores around the house to earn money to care for the snake.
Get EVERYTHING YOU NEED except the snake and the food yourself. It's not alive, so they shouldn't really stop you.
caging (rubbermaid or glass tank, glass tanks suck at holding humidity though. Just make sure it is SECURE)
heat pad
lamp dimmer
digi thermometer
some kind of hide (soda box, cereal box, it can be free)
news paper as substrate.
Get a job, so they don't have to support it. If you have a room of your own, put a stopper on the bottom (it goes all the way across the bottom of the door and touches the floor) so if there is an escape the snake can't get out.
If you have vents put 1/4inch mesh over the vent so they can't get out there (make it look NICE for your parents sake).
Make sure any holes into a room outside your own are covered! So if the snake is loose, the only way it can get out of your room, is if you leave the door open.
if nesecary put a padlock on caging with a key, keep the key on a piece of leather around your neck or keychain.
Litterly make a written agreement that you will take care of the snake (VET visits, feeding, etc..etc..) and that if you can't you will get rid of it, and that you agree NOT to show the snake to your parents unless specificly asked to see the snake.
Make witnesses sign it and everything.
EDUCATE THEM on the snake, it's natural history, husbandry issues, morphs, prices, impress them with knowledge and maturity.
Don't shove it in their faces.
Leave printed pieces of paper or books about ball pythons laying around the house. They may surprise you and start reading it.
Good luck!
-----
1.1 Ball Python, 0.1 motley amel corn, 1.0 western hognose, 1.0 red blood