You're right in saying the club can't just give us a song and ask us to sing it. That approach is too forced.
I think for this to work, it would need a decent-sized group of fans to start singing it (e.g Brigada 1874). They'd have to keep persisting with it, and I think it would be a massive struggle at first, but it may eventually catch on.
It won't work if people sit in their seat at VP and grumpily dismiss it, thinking "this won't work". The more people that get involved, the more it will encourage others to sing along.
I'm sure the whole KOP never just stood there one Saturday and suddenly erupted into a rendition of "You'll never walk alone". I guess it was a very slow process whereby some of the fans started to sing it, others noticed and gradually started to sing along, and eventually it became their anthem.
FWIW, although 'Stand By Me' has nothing to do with Villa, I think it would be amazing if you had most of the ground singing along to it, flags and scarves raised. It would add an amazing atmosphere to VP. It won't work, though. We're Brummies. We're too miserable to get something like this going.