How can i convince my parents to let me get my lip pierced?

Ok, now please on comment saying what would you want to that for or any of that. i'm 13 (and yes i know you think thats to young) I asked my mom last sumer at age 12 to get my nose pierced and she said yes however my dad wouldn't let me, only that summer my mom told me she would rather me get my lip done then nose. So i asked for my 13 birthday and she said no becaue i am to young (doesnt make any sense). But i've waned to get it done for so long, i am responsable my parents trust me, they always say i am a good kid, so please dont tell me anything like be responsable. My mom hates facial piercings, my dad just thinks im to young. I was thinking of maybe writing them a persusaive letter, what do you think? And if i do should i suprize them with it or try and make deal say somthing like,"how about you give me the chance to persuade you with a letter" i think they would both be impressed with a letter. Do you have any other suggestions,or ideas for the letter? Any tips or anything would be very helpful thank you!