About 50 years ago we saw a movie with Farley Granger playing a spoilt rich boy/criminal who was being transported across country and he convinced his guards to stop off at his mother's house (mansion really) so he could sing a special birthday song to her. It was a ploy to try to escape (and I don't remember if it worked) but she was having a big party and Farley Granger did sing to her and the song has stayed in our memory banks ever since. It's sung to Twinkle twinkle with a slight modification at the end:

Happy birthday Mother dear,
You will always find me near,
Close to you year after year,
Happy birthday Mother dear.

I guess it was written by a script writer so doesn't really qualify as a genuine birthday song but we used to sing it, and even tho' we've forgotten the name of the film it was in or how it turned out in the end, my sisters and I remember it.
Robyn