You could also post an ad yourself on a site like gumtree (or the american equivalent) asking for an older, disabled bird. People might not advertise if they have one that they d potentially like to rehome thinking that no one would want them as mentioned above but they might respond to an ad specifically asking for one.
The young budgie we adopted from a rescue shelter here has a leg deformity and I was surprised to find that no one had shown any interest in adopting her while she was with rspca (according to the staff) considering that there are so many homes who actively advertise that they are looking for birds to adopt in the UK. Maybe it's because her deformity though I can't be sure of course.
I really hope you will find one of these budgies to give them a good home. Best of luck.
Edit: apologies, I realised that I basically said the same thing like beth. I should really start reading all posts in a thread be fore replying..