Warning: A slingshot is a dangerous thing. Please do not show your child shooting with anything but paper balls. Please keep your child under observation while using the slingshot. Furthermore, the slingshot can "backfire" if it breaks, or if the shooter looses the grip on the handle, so make this clear to yourself and your child before using it. (I take no responsability for injuries caused by things you made!)
I loved shooting with a slingshot in my childhood. Now I will challenge my son in marksmanship in our living room.
Note: I had some moral trouble designing, making, and publishing this slingshot. If several of you out there find it deeply inappropriate, I will understand it, and remove the thing from Thingiverse. Do not hold back on expressing such views!
Print the part with any suitable resolution, but sufficient material. Shown is one printed with one perimeter, one solid layer, and 0.4 infill.
Cut some piece for paper ball cradle; shown is one cut from a 10mm PVC tube. Attach a rubber band between each side of the cradle and each pole of the slingshot.
Please do not scale it up, or use too strong rubber bands. That would transform a dangerous "toy" into a dangerous weapon!