You have the right idea, but come on ! This clearly isn't about a cover story, IMO they're all BS. You don't have to lie, you have to be good with words. it's all about CHARISMA. Charisma is my favorite topic!
There's a lot about this.
If you wanna get a better chance at this, there are a several things you can do. First, watch your tone. Do something that suits you, like speaking in a sweet voice, or in a confident voice! Make it look like you know what you're doing and that you're prepared to go out without messing something up. You're a DJ, after all!
1. Be in a good mood! It's hard to reject someone like this.
Your parents can't help but to be sorry! Be good cute that they have to let you go.
2. Wait until your parents are at a good mood too!
3.
"Making pepole doing what you want them do it is a matter of telling them what they want to hear!"
Tell your parents that you're giving them a break and that they should let you out so they have a chance to relax tonight as they want to.
Keep pushing at this. Tell them stuff like: "Oh, come on dad... Isn't it going to feel sooo good, you know, to just laaay down on your couch... just enjoying your wonderful rest... *in a smooth voice* Then keep adding details!
4. the lowest thing you can do, (So don't do it often) is to make your parents feel bad about not letting you go. Tell them that all of the other kids parents let their sons go, and that it's really lame that they don't let you go. I would make them know that I would really want to go too!
I don't want to confuse you or anything, so be warned! Do at your own risk. I hope you have a general idea.