But he won't sit still. Competition may be the answer.
So your young one is a busy beaver. You don't think he, or she, would ever sit still long enough to do something complicated like write a short story. Who is really saying no here? The child? I think not.
Take a deep breath and stop approaching the problem the same way over and over again. Let's call him/her Lesley for sake of argument. Lesley is an active, healthy, 10 year old that has not been diagnosed with ADD or other similar condition. I won't deal in this manner with a child that actually needs therapy. It is up to his parents to recognize that there may be a real behavioural problem or learning disability and address it using professional help.
OK he's 10, pretty bright, energetic... almost too much so, but has lots of untapped potential. What can you do? You need to act. I like to use writing short stories as the task since it offers so many benefits being such an active versus passive activity. The individual must apply lots of mental energy and gets lots of skills improvement in return.
Lesley won't write, or do whatever, so you will have to turn the tables. Typically, if you say do it, it won't get done. If you plead, it won't get done. If you threaten with punishment, it may get done but the work will be sloppy. What will make Lesley write a short story? Well first, what is it? The task that is. In this case find a brief story, and read it to him. What's good about it? OK, review what happened, the emotions, the scene, the characters, the drama et cetera, and see if he can relate. Now let's skip to other tasks.
Show the task in order to explain by example. Do not preface by saying you want to show him this or that 'because'. No, just say 'have a look at this'. Never set up for the fall. If you release motivations to a young audience, they will find ways to balk and defeat you. Let's say it's cutting vegetables. Not the best choice? Uh... did I say the knife was the best one in the house and we were cutting carrots or turnip? No, you have to do some work here too. It's a butter knife and he's slicing Zucchini. Set limits if you must, but start trusting if you can. Expect more and you might get more.
First you show him, then you ask if he thinks he could do it, and then he does it. What happens next? He shows it to you. Fine, I wouldn't eat them either, but you get the point. You challenged him, a bit underhandedly, and he rewarded you by requesting approval. This tiny bit of competition reeled him in!
Now, back to writing. So you read to him, and talk about the story. Now ask if there is something he can write about to make an even better story. Chances are this little challenge should be enough to spark an interest. If the story you chose to read had been written by a stranger, this little bit of competition won't be negative. It should produce a healthy drive for success, to be better than before. And Short-Stories-Help-Children.com is all about making children succeed.
Peaking someone's interest in this way is done all the time. Competition is often merely veiled and hard to recognize. Might as well use the techniques while you can. The advertising moguls will get the kids later anyway.