As I am a music educator, I would truly value if my birds would sing a song. I've done alot of searching on YouTube for singing parrots and find that in general, even the most talented birds, like Einstein (the African Grey that's been on TV) only sings ~part~ of a song ("Happy birthday to you" is about it).
I am somewhat convinced at this point that even if the melody of a song is simple, too many words make it rough, or vise versa, a simply-worded song may have too complex of a melody. I suspect we need both a simple set of easy words with a simple melody for them to be successful at it...and if it happened to be something the bird found fun to do, all the better.
As much as Tamber is a well gifted talker, he doesn't sing anything. I do whistle a lot around the house and he will try to imitate me with a single pitch here and there. Unfortunately, all he has mastered right now is a wolf call (which I did not teach him) and the slurred three-toned whistle we use to get someone's attention (the sort of "Hey, look over here whistle"). I have been trying to teach him the two descending tone whistle we would use to say "You who!"
I would really like for him to be able to do something more significant, like maybe the first line to the "Bridge Over the River Kwai"...but I suspect this might be way too much!
So far the best I've heard was an Eclectus whose owner sang opera. Knowing how much practice the owner had to be doing to have the voice she had, it was no surprise that the Eclectus could do some very nice vocables. (Vocables are non-sensical syllables singers will use for warming up.) I've also heard a similar thing from a macaw; however, the macaw was significantly off pitch and had an uncontrolled tremolo.
If anyone is successful and getting their bird to do a full song correctly, I'd be very interested to hearing about it.
Deb