See if you can find a Crosman 760.
Older is better, old enough to have wood furniture, best of the lot!
Multipump Pneumatic, so power output relies on power input. A couple pumps is good for back yard shooting. 10 will do a number on a squirrel, if you wanted to. Rebuildable with a pocket tool and about $12 worth of parts, till the end of time, almost.
The older ones with wood furniture are more solidly built, the newer ones use more plastic, but are still a pretty good deal. Over 12 million of them out there, and still in production. Gotta be something to that.
Another option (pricier) is a Daisy target BB gun. Single shot, #### and then drop a BB through the muzzle to load. Accurate. Used by the JayCee's in the States for their BB gun marksmanship competitions. See D and L Airguns site.
Less accurate, but still fun, a regular Daisy BB gun.
Safety glasses, reactive, non ricochet prone targets and backstops are a must, though, for the BB guns, although an old bedsheet hung over a cord will do, and if you hang it right, you get you BB's back, too. Loose paper wadded up into a box (got a moving Company around? Lots of boxes and packing paper) works good as a recycling backstop too, to re-use the BB's.
The newer spring piston airguns may be a bit much to handle, for a young-un', or not.
Try to stay away from the CO2 guns, on cost alone, as it'd cost about the same to shoot a 22. Consumables are a PITA, unless you can hack the hardware to build a bulk system on the cheap, to use paintball tanks.
If the kids are a little larger, consider one of the Daisy 853C's. If they miss, it won't be the rifle's fault!
Cheers
Trev