My mom sang this song to me.. but the lyrics were slightly different and she personalized it with my name and the color of the bird..
Little BLUE birdie in the tree, in the tree, in the tree, little blue birdie in the tree, sing a song for (name, e.g. Dan-na)
Sing abut the roses on the garden wall
Sing about the posies growin' there so tall...
Little Blue birdie in the tree, in the tree, in the tree, little blue birdie in the tree, sing a song for (name e.g. Dan-na)

Next verse I'd pick another color...
Little RED birdie... etc.