The 135gr Sierra Match King loaded to Hodgdon's YOUTH load of H4895, or IMR's YOUTH load of IMR4895, in conjunction with a muzzle brake
and *GOOD* hearing protection should allow pretty much any youth to handle a short barrel 308. The awesome thing about 4895 is that you can load it so extremely far down.
H4895 @ about 36.5gr with a 135gr. SMK according to hodgdons YOUTH LOADS reloading data. This data is available from their homepage under: DATA / YOUTH LOADS.
Have a good one,
P.S. they have youth loads for many different calibre's, including .243.