I've made sooooo many mistakes trying to find kid friendly guns.
I went with a lil badger. Big mistake. Anything with a hammer is too difficult for lil fingers to manipulate. Goes for shotgun singles as well. Accidental discharges are terrifying but with kids, holy jeezus fk, I still sweat thinking about it. Muzzle control FTW.
Tried a single shot cooey, can't remember the model ATM but you had to manually pull back the bolt; perhaps the Ace. Same problem as above.
I grew up with the cooey 60 so of course there had to be one in the stable and that was my "winner" with kids. I am still in love with that rifle, but LOP was a problem for small frames. I'd cry a little if I had to cut down a cooey. It wasn't that big a deal as kids prefer bench over offhand and I let the smaller ones sneak it into their armpit rather than properly into their shoulder. (already feeling the flames, I'd teach the proper stance, but in the name of fun, I'd let the tiny bodies override me)
NO SEMIs. You'll never be able to grab it out of their hands in time if there is an operator or mechanical "malfunction". Also not a fan of levers for kids as they have a tendency of swinging the muzzle around while struggling to reload, and they're much slower on a bench.
By the time I'd made almost every mistake in the book my boys & their friends were big enough that LOP wasn't really an issue. They grow up quick. Scoped Marlin 60 ftw once LOP isn't an issue. Marlin 795 was their favorite once I trusted them with a semi.
Sorry, I can only tell you what not to do. I regret not having went with a purpose driven gun like the rascal. Also don't discount the red ryder. Like SKS's most are mid, but some are exceptional; ammo is cheap and all that matters is the smiles (and teaching safe handling which can be done with a bb gun, and I don't sweat watching them struggle with the lever as much). Plus you can shoot it many more places than a 22 - so more smiles.
(EDIT: one more plus for the Red Ryder, some parents don't have firearms experience, so are frightened about what they don't know. The RR is a christmas story toy so I can get into the hands of children with overanxious parents allowing me to teach safe control to those that would otherwise have zero exposure to proper handling.)