There are two solutions to your problem. Both involve an image editing program.

The first is to edit the image and add a fake sky to replace the washed out sky. The other is to save the photo as RAW format. This will preserve all the original shot information. You can then selectively apply an EV (exposure) change to just the bird leaving the sky alone. This should make both parts of the photo a similar lighting.

If you are photographing an object you can control (like a static object or a person), a third option is to reflect some light into their face. But that will be almost impossible with a bird shot.

Good Luck!

I often have opportunities to shoot birds perching on the top of trees against a bright blue sky. Naturally the birds are black, or very dark, when shot. I tend to over-expose the shots by up to 2X, in which case I get the birds in their natural colors but then the beautiful blue skies become washed-out. Any tips on how I can have my cake and eat it?

Thanks for your advice,

Winston