How do I Fulton child soldiers?

You don't actually need to research the Child-Safe Fulton Device to Fulton the kids.

What you can do is call for a jeep - Soviet or American, doesn't matter - stack three kids in it, and then call for another Diamond Dogs vehicle.

Diamond Dogs vehicles are, just like D-Horse and D-Walker, rigged to Fulton themselves when their presence in the combat zone is no longer required. This costs you NOTHING. They auto-Fulton themselves when you call for a new vehicle.

This is actually the most economical way to get people out, ironically. Every vehicle has a dirt-cheap 1,000 GMP deployment cost (fair warning: this may be related to the cost of your helicopter calls, I use the cheapest helicopter because I'm a tightwad.) Thing is, 1,000 GMP is only 100 GMP more expensive than the cost of Fultoning three guys by themselves! And it cuts your Fulton usage down to precisely zero, meaning you won't have to call for more Fulton devices mid-mission, which can save you an absolute truckload in the long run!

Side Ops 113 unlocks the child Fulton.

To unlock the Side Ops, you will have to complete Mission 26.

You can place them in vehicles and fulton those.