This is by no means a guarantee, but this might help to pull the sword from the stone,
1. try to see if a CM is around watching
2. A photopass photographer being there helps.
3. A lot of time the littlest or the youngest one in your group gets to pull the sword. So if you want your 8 year old to pull the sword but have a 4 year old with you, try taking the 4 year old out of the picture by having someone sit with the 4 year old somewhere.
4. Have the grown ups or older kids make a big ta do about how they surely will pull the sword from the stone because they are bigger and stronger and make sure the littlest one goes last.
I think the CMs like to pick the people that go along with the movie, where Arthur was able to pull the sword even though many other bigger, stronger men tried before him.
Again, this is no guarantee, but this is the pattern I noticed. I know there are plenty of exceptions, but again, when this question comes up on the Disboards, this is the pattern.