Whatever fits his hands...
If Rimfire is allowed, then the MKII wouldn't be a bad choice. The mags won't drop freely without assistance, but installing an extended mag release and an extended bolt release from Volquartsen would really be a plus. And with practice, you'd surprised how fast his reloads could be. The hunter models have the fiber optic sights. A real plus if you can add them to your pistol if those are allowed.
Other rimfire choices- A Browning buckmark. A better trigger out of the box, and the mag release where it should be. Better sights? Even a S&W 22A would be good, but he'd probably out grow the durability of something that's got aluminum parts.
To jump up to .380 if that meets spec for your matches would be a Colt Mustang or Colt Government series 80 .380. (Not a full sized Government model 1911) There are near equivelants of these in different brands, but you'll have the best resale value with these when he out grows them. Stay away from the 'pocket' .380's. Many of which are DA anyway.
If he can shoot something bigger... A Colt Commander or an Officer's ACP in 45acp with lightened springs and light loads might just be the ticket.
If you've got more money to spend, there are several smiths that build .38spl and .38Super 1911's. -Even some factory options. Oh OK, even one of the smaller 1911's in 9mm. I would stick with a single action semi-auto. If nothing else but for length of trigger pull and you can get slim grip panels for the 1911 series. And the Commander/Officer series has the grip safety that the Mustang and series 80 .380 don't have.
Buying guns for kids isn't quite the same as buying shoes for them, but close. Thankfully they outgrow the shoes much faster. I try to buy guns for my boys that they won't outgrow any time soon. So, in your case, a Commander sized 1911 in 9mm, 38spl, 38super or 45acp would be something they could shoot for years to come with options for the frame, (swap the top), down the road.
If he's got longer fingers for DA pull, don't rule out a revolver. A good many of the smaller framed S&W's with 3-4" barrel would be great. A Colt Diamondback too. Speed loaders are readily available for them. .38spl with wadcutter loads would be quite managable.
I guess the key is, what ever the Range Officer and your local club match rules allow. If they'll allow the rimfire for a junior for practice and gain experience until he's big enough to run the bigger guns, I'd go with that. When he starts beating the slowest adult competitor that's shooting centerfire, it might be time to bump him up.
-Steve