The young, adoptable dogs go very quickly, usually to people to have already submitted an adoption application and been approved.
Your best bet is to go to Petfinder and find Yorkie rescues that adopt in your area. Then fill out an application so you will be considered when the perfect match comes into rescue:
Petfinder.com: Adopt a pet and help an animal shelter rescue a puppy or kitten.
Just my two cents....
Financial constraints are not a good reason to turn to rescue. Adding a second dog is a big financial commitment no matter how you get it. Also, since rescues have unknown backgrounds, you may face vet bills or expenses for trainers to deal with "baggage" a dog may come with.
I adopted Lady nine years ago this month. She is my heart dog, my soul "malt", but her vet bills have always been outrageous. Please make sure you are making the decision to rescue for the right reasons. If you do, I promise you will never regret it!