You might want to check online pet ad sites. One of my biggest gripes with rescues is that they make the adoption process so difficult, that many of the birds never get to leave the rescue. (If you live a 3-hour drive from the rescue and work a full time job, how the heck are you supposed to visit the rescue multiple times per week for "at least 3 months" without neglecting your own birds??? it's crazy)
However, a lot of people put up ads on online sites before they resort to a rescue, so you can often find a bird in need of a better home, better cage, better diet, etc. One of my ringnecks was in a toyless, perchless cage eating nothing but tropican pellets and no human interaction for a year before I bought her from craigslist. I'm pretty certain they never even let her out of the cage, because her flight feathers had grown in but her wing muscles were too weak to fly at all, poor thing. So, if you can't adopt from a rescue because they think you have insufficient prior bird experience, maybe consider online ad sites (craigslist, hoobly, etc)