The load I use - for light 20ga loads is ---- 2 3/4" STS hulls .... 12.0gr Hodgdon International, Win 209 primer, WAA20 wad. I substitue the Orange Duster wad / as a direct substitue for the WAA20 wad.
But this load will give you 1150 fps / 9,000 psi pressure .... so its about as soft as you'll find..
The load range on this recipe is pretty good / the Hodgdon book also lists a load ( 3/4oz again / at 13.2 gr of International at 1200 fps ) ....so you can go from 12.0gr to 13.2 grains ( as he gets stronger / and older ) ....
On the light end of this load / its basically a 28ga load in a 20ga gun.
But I find with these young kids / its more about upper body strength - so they can swing the gun a little ....so using different guns, getting something real light ( if you had a semi-auto / might be ok ) ....but like others said, if he can handle the weight, adding as little as 1 lb to the gun can reduce the recoil close to 20%.
Having a lot of grandkids myself .....I went to a local sporting goods store --- and picked up 3 or 4 vests from XS, Small, Med, Large ....etc so I've ended up with a vest / with a good recoil pad in it ....( and then I can pick a size / that fits them as they grow). Some vests are both left and right handed / some are either lefties or righties ....so I managed to get some that had recoil pads on both sides.
Pick a day at the club - if you can - when its really quiet - so you can get your own field and work with them a little ....
A couple of guns that I use in 20ga for new shooters....is a Browning BPS Hunter model, pump with a 28" barrel ( its about a 7 lb gun ). Another one, is a Benelli Super Sport model in 20ga ...with their comfort tech supression system in it ...is only 6.3 lbs and its got the cool carbon fibre look to it - the kids like it ). Some kids at 11 are big / some have arms the size of my thumb ...so every kid is really different... You really need to adapt / so they have a good time.