There are a few pointers I would give you:
1. Don't beg. Show a willingness to work and earn. Show them that you appreciate the value of a dollar. Maybe stop spending money on a few other things that you spend on now (if you do)....maybe tell them you'll save up by not going the movies for the next few months, etc. It shows you are serious.
2. Show your parents how much research you are doing on what you need and what you are going to get, and that this is not just a spur of the moment decision. Show them you are spending wisely.
3. Point out that fishkeeping is a very scientific hobby, combining chemistry, biology, even physics. You LEARN stuff by keeping fish...much better than a video game or spending $180 on the "right" pair of Nike shoes.
4. See if you can work it into your school work, maybe writing reports, etc. Point out that the experience you gain might even be setting yourself up for a job at a
LFS next summer (or some time).
5. I've got two kids myself now, and I can see the impact that hobbies like fishkeeping have on them. Point out to your parents that you are learning responsibilities, you are planning ahead, you are actually learning something in your free time....parents love that stuff!
When I was a kid, I was always into "sciency" stuff. Not fishkeeping exactly, but I worked to save money to buy stuff like telescopes, microscopes, chemistry sets, ferrets, etc. I'm sure my parents didn't get it, but I worked hard around the house, got summer jobs, and earned it.....guess what....I actually did become a scientist...so I guess it worked out!