The best thing to do is to hope for consistent lighting and use manual exposure. Facing the direction in which the birds are, hold your hand up in front of your face with your palm facing towards you. Point your camera at your palm, making sure you fill the metered area with your palm. Make sure you are not casting a shadow over your palm. Meter off your palm and set your exposure to be about +1 to + 1 1/3 stops above the centre point of the meter.
So long as the lighting does not keep changing (e.g. sun breaking through clouds every now and again) that setting should keep you sorted out nicely. It won't matter what colour the birds are or whether the background is bright sky or dark forest. So long as the birds are lit by the same light as your palm you should get a good exposure for the bird(s). If the birds are outside and you are in a hide, or a shaded spot, then you will need to go outside to get a reading under the same lighting conditions as the bird(s).
This is just like metering off a grey card, except you need to go +1 to +1 1/3 because your palm is paler than a grey card. You use your palm because it does not tan and so is a consistent tone throughout the year. It's also cheaper than a grey card, more convenient, and you always have it with you. Just don't try to use it for white balance 
Another approach, again using manual exposure, is to use the Sunny 16 rule and its derivitives to set a manual exposure depending on the light conditions. See explanation here....
http://medfmt.8k.com/mf/sunny.html
So, for example, on a sunny day you could set f/16, 400 ISO, 1/400. That would give you a fair DOF to give a margin for focus errors but maybe not quite enough shutter speed to freeze motion or camera shake. So how about f/11, 400 ISO and 1/800 or f/8, 400 ISO and 1/1600. In less than optimum lighting you will need to make adjustments as per the guidlines described above for cloud/haze etc., but by using manual exposure you will at least prevent the meter being fooled by odd backlighting and other backgrounds. You will also get consistent exposure regardless of whether the birds themselves are black, grey, white or anything else.