The thing you may want to remember is that unless your parents have some martial arts background, they will probably not have a very realistic or informed knowledge of what martial arts actually are, let alone specific systems. So you may find that while your parents are opposed to one approach (Can I learn Ninjutsu?), they may be open to another approach (Hey, can I take up Judo? It looks like a great sport!).
When I was (much!) younger, about 10 or so, I asked my parents if I could learn Ninjutsu, and was told emphatically "NO! It's far too violent!!!" So I asked if I could learn Karate. "Sure, that's fine". The thing to remember was that the primary image of Ninjutsu and Ninja was one of violent movies, bad guys, lots of weapons, whereas Karate was publicised as being fun, family friendly, and giving good morals (?). The Karate Kid was out around then, just so you know.
Now, with my understanding of these systems, I find this rather funny, as Karate's primary strategy is one of attack, it is forward moving, it's primary stance is offensive, and so on, whereas Ninjutsu focuses on escape, avoiding conflict, and has it's primary stance as a defensive one... but then again, no one ever said my mother knew anything about martial arts. So if Judo is available, try asking in a different way, and see what happens. Who knows, you may get more support than you think!