How do you let your parents let you buy a DSi

DSI's are really expensive- that's the first part. What you need to do is one of the following:
If your birthday is coming up, ask for one for your birthday. You can also ask for one around the holidays- Christmas or hannukah, whichever you celebrate. Or Kwanza, too. (Sry I think I spelt that wrong)
If these two events aren't coming up anytime soon, I suggest paying for it with your own money, or paying it off by doing chores for your parents.
Hope this helps! :)