Have your parents said why they don't want to get you one right now?
Do you have a steady income or will your parents being paying all of its bills. (and there can be a lot of them)?
The list of "qualifications" for this dog is very long and most people who have trained a Yorkie to the extent probably aren't going to rehome them.
house trained,
fixed,
obedience trained,
good with people/dogs/cats,
hardly barks
With the exception of being fixed, these things can be difficult to achieve.
Yorkies can be very stubborn.
Are you sure you can't wait a few more years and buy your own Yorkie?