My daughter takes piano lessons at a university in their preparatory program. Normally, they accept beginning students between the ages of 5 and 8, because over long years of experience, this age window is what they've found to be optimal. They willingly accepted my daughter late - she was 9 when we started. She had fine motor delays that made starting sooner impossible - it would have been too frustrating.
They do recommend that children be capable of sitting still and focusing for the 15 minutes a day beginners need to spend practicing before they start. I would add that it is important for the child to have sufficient motor control. If the child can write letters and numbers adequately and without struggle (not neatly, but at least legibly), he or she would probably be able to enjoy playing a piano.
I do think that perhaps the most important criterion should be whether or not your child wants to learn to play. There are sneaky ways to encourage this. Start taking your children to live performances whenever possible. Explore across genres - classical, symphonic, jazz, even country and pop. Always point out the piano/keyboard player, and talk up how cool you think it is that that person can play. If you have friends or relatives whose kids play, get them to sit down with your child and noodle around on the keys a bit, and maybe even teach your child an easy piece or two. And YOU should play for them, even if it's just "Twinkle Twinkle." It has been many years since I've practiced enough to be any good, but my kids still love it when I play. My daughter's piano book has some duets, and we play them together. I learn my part right along with her, and she gets to see me needing to practice, making mistakes, working out the tough stuff, and having fun playing with her.