You can absolutely develop your ear. While I'm not sure you can train yourself to develop perfect pitch, I've noticed that the last year or two I've been getting a lot better at just blindly guessing the key of a song and getting it right. Even when I have to poke around for a second to find the key (which is most of the time), if it's a rock, blues or country type song I can usually figure it out by ear quickly. I could not do this when I first started. Not even close.
IMHO, it's just like any other skill - you need to practice diligently. There are a lot of relative pitch training systems out there, but you can also just start working on trying to figure out songs by ear. That's probably the best thing. The key is to pick songs (or just melodies) that aren't
too advanced. You probably know "Happy Birthday" or "Jingle Bells" - try that first. Then try working out solos to songs you like. This will do a lot more for your ear than playing chromatic scales over and over. That said, you can work on getting the sound of each interval in your ear - that will be very helpful.
"It doesn't take talent to upgrade your playing. It takes patience" - Kenny Werner
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