Check out the Sprockids and Trips for Kids websites - clubs/rides have started out from those two organisations, altho' Sprockids seems more suited to your needs, even tho' it's based round mtb'ing.
Don't worry too much about road/circuit racing - just get him into racing of any kind: bmx, cyclo-cross, mtb, etc.
Start your own club if necessary - kids clubs can get by on a patch of grass about the size of a soccer field.
Concentrate on skills using free/cheap equipment - small, sand-filled drinks bottles, planks, pallets, make seesaws (teeter totters?). Create skills certificates from simple stuff like:
Slow-riding (15m/yds in at least 60 secs
Riding in circles
Slaloms (through aforementioned drinks bottles in straight or zigzag lines with bottle lines of decreasing distances apart (e.g. 2.0m, 1.70m, 1.50m, etc); get them to ride one-handed (each hand) through the slalom course
Track stand competitions (10m.30 secs for one of our 10-year old girls - irritating child!)
And so on.
Put on local off-road family rides if possible as way of recruiting like-minded people
Get local club to organise a circuit race (local park?) for kids on mtbs (or diy)
The sky or your imagination is the limit
and it's great fun.