It sounds as if you might be looking for a gun with a shorter length of pull that would be a better fit for a youngster. If so, Browning offers a "Micro" version of their A-bolt that comes with a nice wood stock and the Browning reputation, making it a nice heirloom gun. The new Mossberg Patriot is also available as a "Bantam" model with a shorter stock and length of pull for youngsters, or even adults looking for a gun with a compact feel. These Super Bantam rifle includes a synthetic stock with multiple extensions that allow you to lengthen the stock as the child grows. That opens another option, to purchase a full size gun in which youth stocks are easily available. That way, the youngster can use the gun with a youth stock first, then replace the original full size stock later.
Keep in mind too that reduced recoil ammo is readily available from multiple manufacturers. For example, Remington's .270 reduced recoil ammo produces less recoil than standard .243 ammo. Going this route, you could purchase a full size rifle in a larger caliber and use the youth stock and RR ammo when they are young, and still have a more adult-size gun for later use.