How can I get my parents to let me babysit?

Ok so my boyfriend has been asked to babysit his mom’s friends two little boys this Friday night. 7:30pm til late. Their Dad said be could have people over and he asked me to help him. I met the kids a few times before and they’re so cute plus I LOVE minding kids!! My parents know this and that I’m really good with them. I really want to be able to do it but my parents can be super strict and funny about things. I want to explain to them that the parents want 2 people minding them and that everytime my boyfriend minds them by himself, they exhaust him. They’re hyper things + he can’t ask any of his friends because they either live too far away or are grounded. I know my parents will want to say no on the grounds of the fact that they don’t know these people (they said before that I can only babysit known people, but I’m nearly 18!!) + the fact that I will be with my boyfriend without adults in a house. They don’t think that I would have sex and know I’m respectful and think I don’t drink but still I don’t think they will be convinced by me saying that I’ll be busy with the kids the whole time and that they will be in the house!! XD. My parents are awkward and can’t say that they think I’ll get physical with my boyfriend so I want to assure them. Also I was thinking of getting the parents to call my parents and get my parents to drop me off or get my boyfriends parents to call mine to assure them buuut…eventhough we’re going out a year and a half, our parents have clashed a lot, especially my dad and his mom on the phone because she’s a hippy and he’s “proper” if you get what I mean. Traditional. And the kids parents are hippies! :/ Oh god just anybody give me ideas and ways to convince my parents this is a good idea!! How should I go about it? What to ask or tell them first??