There's no foolproof answer, as people have all kinds of vocal ranges, and "Happy Birthday" is actually a relatively difficult song for novices to sing because it contains a full octave leap. You may enjoy this article by a music professor at Penn State:
As part of our work, our colleague Peter Pfordresher, of the University at Buffalo, shared some data with us on college students singing “Happy Birthday.” Some of the students started the song high in their vocal range, more started lower in their vocal range, but many of them failed when it came to the big ascending leap: the third “happy birthday.”
This is what makes this universal song so difficult for people around the world to sing. The third “happy birthday” has an octave leap, meaning a seven-note jump in the musical scale. It can be hard for people to manage, especially if you started too high in the beginning and have already topped out your range.
Having said that, since the range of the song is the octave from low sol to high sol, a key like F major or G major should minimize discomfort for the greatest number of people.
In G, men can sing in the lower octave and the highest note will be D above middle C, which is at the high end of my range but doable. Women would sing an octave higher, and the high D doesn't seem to be a problem for most women either. Of course, those with vocal training will sound better.
I have heard anecdotally that "there was a study" in which groups asked to sing the song tended to converge on G or G♭ major, but I couldn't find a reference.