From a parent's point of view, they are probably worried about extra work or expense for them.
Therefore, if you want to convince them you will follow through, make sure you are meeting all your responsibilities at home and at school. In other words, the maturity of your actions will mean more than your words. Vote with your feet!
Being a parent, admittedly of "elderly" children who now have their own children, I can assure you that acting in a mature way will get you lots further than begging and wearing them down.
You are a bright young lady, keep up the good work. Hope you get your chickens!