Since this question was searched on GWGT, without an answer I might add…
I guess some ideas would be ear plugs, shutting windows, turn on a fan for white noise, pop in a CD of background noise like rain, and even move to another room. But a bird singing at night is usually by an unmated male. Once they get the girl, the singing stops.
All birds are protected by state and federal laws, and nothing can be done to harass them, no matter how annoying they are at wee hours of the morning. It is best to ignore them, or just plug your ears. The worse noise in my opinion is that early rising woodpecker hammering at 4am. Birds like mockingbirds can try the patience of even the most diligent birders since they mimic and can sing all night. Lucky we don’t have them here, but did in a place I stayed for a few weeks. They are a noisy bunch.
I don’t mind the bird songs, but do have to admit, many times they waken me long before I am ready to rise.