Well, I have been thinking about small and light rifles lately too. My little boy will need to have something in the next few years, and I can't think of a better reason to dream up a fine rifle for him.
This is what I had been thinking about:
Mini mauser action with a slim and trim wood stock. CZ and Remington 799 both make these models. The Zastava has a 2.37" magazine, and is available in the .473 bolt face (22-250). I am thinking a rebore/chamber or rebarrel to one of the following: 6mm BR, 6.5mm BR or 7mm BR.
Consider the 6mm. With 23-25gr of powder under a Speer 85gr BT spitzer, you would get around 2800-2900 fps. This is about 10gr of powder less than what a .243 would need to achieve the same velocity.
Recoil in a 6lb rifle would be 5.9lbs in the 6mm BR, compared to 4.1 in an equal weight .223. In a 6lb .243 with full power 100gr loads the recoil is about 11.5lbs.
The performance seems pretty good too. At 2800fps with the noted bullet the point blank range of the 6mmBR would be 274 yards! This is, of course a pretty long shot. At 200 yards you still have +2300fps and 1058 ft-lbs of energy, plenty for poking a hole through the lungs of a Blacktail, or Whitetail for that matter. And with the construction of the speer bullet, you should get good mushrooming at that velocity.
The other neat thing is loading the 6mm BR down with 55gr bullets. You would burn about 2 grains more powder (in some cases equal or less powder) to achieve the same velocity as the .223 with 55 grain bullets. This means the recoil and report should be very similar to a .223!
How about max performance on the 6mm BR? Well, try a 95grain Partition or Ballistic tip at 2900 fps burning 29-30grains of powder. This is only 100 to 200fps behind a .243, but it uses about 10-15 grains less powder. You have a point blank range of 279 yards - at 300 yrds 2190fps and 1011ft-lbs. I am certain that load would be enough for deer, sheep, black bear and the like at any reasonable range a youngster might shoot.
Just my 0.02!