I got my first rat kinda young, after a long persistance.
Well, I was 14 when I decided to get serious about wanting a rat, I had had about 8 hamsters growing up, and my dad always called them rats and the thought occurred to me one day when I was like 12 or 13 I think.
A while after my hamster passed away ('Dusty'), I started asking for a rat and got to hear "You're NOT getting a rat.." like 5 billion times from my father.
(Hmm kinda like when I came home w my engagement ring he said "you're NOT marrying Richie..." LOL).
Anyhow.. I saved up a bunch of money from b-day an all, and then I got into babysitting for money. I babysat at the firehouse meetings every Friday night and I watched a kid every Tues and Thurs night.
I got a bunch of money and then started asking my parents if they would bring me to the pet store to get a rat, since it would be no costs to them an all.. they would just have to put up with the fact of an animal existing in my room, which I've always had. Then when they always refused to bring to the shop for a few months.. I said for about a week how I planned on walking to the shop someday soon and getting a rat.
So one day I said I was gonna go walk to the pet store and see if they had any nice rats, started walking out the door and my Mom gave in and said she would take me to LOOK.
Well, we got there and the pet shop owner's daughters were desperate to get this one particular rat a home since he was the sweetest and they had held him since he was little, they didn't want him to be bought for snake food. He was a black hooded, and like juvenile sized, he immediately smothered my Mom in kisses and she melted and asked if I wanted him lol.
That's how I got my first rat, Raziel back in like '99.
He was always happy and healthy and pretty much my constant companion around the house. He got huge, but was a big lug. I could even hold him on his back and he always had lots of kisses to give. One morning, about 2 years after, he had passed away, In his sleep overnight just like that. It was one of the hardest losses of my life. My dad's g/f, making nice with me, got me another rat, Ruben, about 6 months or so before Raziel passed. So my having rats just continued on.
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~Anyhow.. you could try finding a steady income, arrange to babysit your cousins every Friday night so their parents can have some "time away" or something to that effect... I started out watching my cousins and then got signed up for a babysitting class which was like every Saturday morning for a couple hours, for a month or so and then I got a babysitting certificate / license which got me more sitting jobs. Or maybe help out a person who runs their own business.. I used to get paid to do inventory and data entry things for my dad's g/f's Ebay and flea market, etc. mini-business a couple evenings a week.
Maybe then if you have an income you could help the "financial situation", like pay some sorta rent or "Rat rent" and also having some steady bit of income would definitely help show you have responsibility. I don't know anyone who would turn down nearly free money. This can also show that you will be able to cover all the rat living expenses every month or whenever you would stock up on food, litter etc. You could even go get hooked up with one of those "savings accounts for kids" stuff some banks do and start an account to save emergency money in. A bank account would also help with the whole proving responsible and serious.
Also, having a small job or two kinda early on is a great start, I got hired at a real store my freshman year of high school because I had experience with my dad's g/f's business and had a ton of references from ppl I babysat for. I was able to save up for my own class ring and afford to go to movies and have 2 rats, a bunny, and a German shepherd. I was able to save up for a prom dress and prom tickets and year books and all that, when my parent's money was tight.. (from the g/f's failing business lol).
Anyhow... I wish you luck, If saying you are going to do things has not worked, showing them might.
~Sorrie this got real long lolz.~
(I got my gecko last June), but I so CANNOT live with the fact that I won't be getting a rat soon! 
