Rod building will certainly be a challenge, not so much because of the cost as for the cost of infrastructure.
In order to build a rod you need the following:
1. rod wrapping jig with thread tensioner
2. rod turner for drying epoxy
It is possible to build these machines fairly cost effectively but they still need some specialized parts. The cost to purchase them is quite expensive.
Building a factory quality rod is relatively easy, though I'm not sure that 9-12 year olds will have the patience to build something that can actually be fished, however.
Also, the parts cost to build a factory quality spinning rod will be much higher than the cost to buy the whole rod at Canadian Tire.
Things get much more complicated when you want to build a custom rod, with accent trim, thread patterns, custom cork grips, logo, etc. Unfortunately these are the aspects of rod building that are interesting and require many, many hours of practice (and failure).
Try Mark at Valley Custom Rods - he may be able to get kits at reduced prices for a boys club.
Other options you might want to consider would be building lures (spoons, spinners, etc), or tying flies. The startup costs for these activities are quite a bit lower than for rod building.