Have you tried spot metering?
Yeah that is the only thing that is going to work for you there, if you want to get the bird correctly exposed. Another things is that i notices that these photos your not shooting with the sun so to speak. If you want the birds to be lit up well you should have the sun in your back this will make sure the birds don't look like they do in these photos.
Depending on the outdoor conditions that your going to shoot in the spot metering might cause you to get a very overexposed sky (you would probably have gotten it if you spot metered the images above) because then your camera would want to use a slower shutter speed = more light = intense sky = overexposed.
I have written an article on metering if your interested. Link here
What mode are you shooting in? Get to know your modedial here
Some tips on exposure here
Along with with understanding your histograms here
Read those and you should get of on the right foot for some nice bird shots