Well, you could have a calm conversation with your parents. Say something like, 'Mom/Dad, I've been really interested in manga lately. It helps me relax and I learn a lot from the different characters and plots. Can I please get some?'
You could start by sharing some of the positive aspects of manga, like the interesting stories and beautiful art. Then explain why you really want to have them. Maybe offer to do some extra chores or get good grades in exchange.
Just be honest and tell them why you like manga and how it can be beneficial for you, like improving your imagination.