"Almost as low recoiling as a .243 "
referring to the 7mm08: It is not physically possible to launch a 140 grain .284 bullet at the same speed as a 100 grain .243 bullet w/o incurring significantly more recoil(theoretically 40% more).
But thay are not going the same speed: the 7-08 is running 100-300 f/sec slower, depending upon which factory is loading it.
Add to that the fact that those published velocities are developed in 24" test barrels ..... which "youth" sized rifles don't have (with the exception of varmit rifles, very few non-magnum hunting rifles do anymore) .... the .243 relies heavily on high velocity for it's killing power .... short barrels found in youth guns cut into that some ..... and make for more muzzle blast in the process ..... the 7-08 also loses some velocity, true, but IME, heavier bullets lose less in shorter barrels than light ones (all else being equal), and rely less on velocity for lethality.
My solution to this problem was to get a 7-08 in as short and heavy a gun as possible, and down load it. Why 7-08? It has the greatest variety of bullets, and when downloaded to 30/30 velocities, is still a lethal deer round, yet with very little recoil ..... yet when the kids get bigger, I can move righ back up in power ...... I already know I can easily drive a 140gr bullet to 2650 ..... There are pretty efficient 160's available that should stabilize in my rifle .....
The only thing that would make my kids' gun better would be a can on the end of it .... but that's not financially feasible at the moment .....
Even if the OP does not handload, there are reduced recoil factory loadings for the 7-08 .... true, the same is true of the .243. The thing is, the -08 can be downloaded for less recoil now...... but later on in life the .243 will always be a .243.