the length of the stock is a bigger problem than weight at that age...
so chose a gun either with a junior sized stock, or one where you can buy a cheap spare stock and shorten it. Or as stated above, a shoulder stock for a PCP pistol (like a P700) is a great option. Chopping a 2250 stock and affixing an adjustable butt pad works well (and the stocks are less than £30 new).
lots of options, but with the exception of the ultra junior, they all seem to require some DIY.
Always looking for any cheap, interesting, knackered "project" guns. Thanks, JB.