There was a thread about "The Gift" a short time back. Also about a Nightingale. Written and recorded by Stephanie Davis, but also recorded by Garth Brooks, Joni Harms, and Aselin Debison.

The Wren Song is a Christmas song and inspired by legend and tradition regarding the wren.

Bird on a Wire by Leonard Cohen and recorded by him and others.

Quite a few songs about bluebirds including "There's a Bluebird Singing" a relatively old song in old time, country, and bluegrass tradition; "Bluebird Blues", and "I Heard the Bluebird Sing".

Good old fiddle tune called "Red Bird".