I've never been a fan of youth model rifles strictly because they are so limited in terms of use. People end up getting 2 maybe 3 years out of them and they end up selling or trading them for something else and usually they take a pretty good hit on the money when they go to sell. In this day and age, there is no shortage of guns that can be useful for kids that they can keep with them and grow into for many years to come or for the rest of their life even.
Obviously, the easiest choice is a collapsible stock AR platform gun. Plenty of kids start out with 223/5.56 with a heavy weight bullet and have good success. If you were opposed to that caliber, you also have 300 Blackout, 6.8 SPC, and 6.5 Grendel that are all very good deer calibers inside 200 yards that you can get in the AR platform. I think the AR is a great choice because you can build your own and get the kids involved in the build process and then they have a sense of ownership in the gun. And an AR can be continually used as they grow up or can be used by an adult until the child becomes "of age" and then you can gift the rifle to them as their very own. Of course you also have the advantage of being able to build the AR into a pistol configuration with a stabilizing brace that the youngster could still choose to shoulder. Then you've got a super short barreled gun with an adjustable length of pull that is capable of firing a lot of different calibers, several which are good choices for hunting, that can be used for a variety of other purposes also. The AR is a huge win-win scenario in my book, especially for a young shooter.
Then another good option is the TC Contender Carbine rifle which can swap barrels. You have the option of 30-30, 7-30 Waters, and 6.8SPC for factory deer caliber barrels or if you want to get a custom barrel, then you literally have close to 100 different caliber options. The length of pull on the Contender Carbine is very short, well within range of a young shooter, but still usable for an adult also. Plus you get the benefit of having a switch barrel design where you can shoot a variety of different calibers or even convert it to a pistol to use also.
Those are my two recommendations for a youth rifle, and that's coming from a gun dealer who sells guns all the time.