well if you do lots of research on chickens (feed, housing, litter mangament, what breed and variaties your interested in) and then display your knowledge to them in some way (write a letter? even an essay?) they might reconsider. if you really are interested in poultry and desperate to have your own, you'll do your best work. if your parents see this they'll know you are legitimently interested in chickens and knowlegable and responsible enough to care for them.
i would suggest seramas. they are a relativly new bantam breed, and the smallest chickens in the world. they are divided into three accepted weight classes: class A, B, and C. they may also be AA which is under 6 oz. and known as a micro serama, or class D which is over 17.1 oz. they go through very little feed and don't need much room-a 18X24 inch cage is big enough for two or three. seramas are very personable, quiet, and surprisingly good layers for bantams of thier size. because they are a little more rare, be prepared to pay a bit more for quality birds. for a pair of traditional type serama (they can also be malaysian and american type, but traditional is the most common and cheapest) expect a price of between $25 and $100 dollars. if you ever get into showing, seramas are a great breed as they are very handlable and confident. just make sure they are true seramas, not mutts, from a reputible breeder. there are severel on here who could help you out.
if all of this information seems overwhelming maybe chickens aren't for you. there's a lot you need to know about them to manage even a small flock successfully. do all your research before you get chickens even if your parents agree, and continue to learn afterwards. byc is a great place for that. we can answer any questions you might have
edit: i didn't see you wanted silkies they are a good choice too. maybe it's just me, but i've noticed that hatchery/feed store silkies tend to be much louder than well bred silkies from a breeder. like i said, maybe it's just me