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.