I agree with GT, lots of punching on the floor. Also, try having them just stand and punch on the springboard--let them get a feel for the bounce of the board. Take a look at their running--they may not be running as fast as they can, and that's hindering their punch. I always enjoy giving them little challenges--having them punch up over obstacles on the floor.
punching of the board is something you wont be able to change a great deal, over a short period of time. Simple because its a matter of the gymnast explosivenes. You can see this simply by looking a group of kids. so will just be better able to punch of it then others.
SO! aside from teaching the kids to actually use their legs don't expect great! changes.
So what i recommend is LOTS and LOTS jumps on the trampoline working on all kids from jumping and landing with bent leg to working just the ankles, working jumps just with the arms. Lots and lots to develop the tension, leg shape, and ability to learn what it feel to stretch completly from them.
Second work the same on the actual board. Hold their hands and have them doing sets of 20 or so jumps in a row. With GOOD form.
Work on them having tight ankles, fast rebounds (keep encouraging it, even though if they say they are trying they hardest they probably are). If they have weak ankles they will not be able to impact the board without their heels hitting the board which means more time spent of the board.
Jumps on floor are also good, however remember to be carefull with not overdoing it, cause the consequence of overdoing it without proper conditioning of the ankles (flexibility and strength) will result in child Osteochondritis conditions to the ankles (eg. severse desiease) and knees (eg. Oschood-Schlatters Disease).
Conditioning like calf raises, theraband work, injury prevention specific exercise etc..
Also one other thing is check that you dont have to many springs in the board if the kids are really light.. i mean for really small kids on a regualar board about 2 spring on the left and right are with at the real bottom is about enough.
Valentin is right with the comments about training plyometrics (explosive power mainly associated with jumping, rebounding, etc.)
I would also look into developing a strong run up to the spring board. Long strides, arms pumping, etc.
Utilising the 'Domino Theory' in addressing problems associated with gymnastics is always beneficial. If the first domino in the equation is perfect then the next steps (or domino's according to the analogy) with fall into place accordingly. Therefore, if the run up seems to be perfect, next look at the hurdle. There are lots of theories regarding the hurdle, but try and perfect it according to what you/your coach believe to be correct. All these suggestions I believe should greatly enhance your ability to strike the springboard with sufficient power necessary for high quality vaulting...goodluck!
At my daughter's gym they put a light colored mat at the beginning of the spring board. This forces the girls to jump over it and really hit the board hard enough. A lot of them still kind of slow down before getting there but they're improving.