You sound a very sensible owner :)
Some pups do growl when suddenly disturbed, and it may just be that your pup is tired and getting too much attention - a bit like an overtired child, he gets grumpy! Also as you will know, some breeds do growl in "talk", I am not totally sure the Staffie is one of these, but I know the Rottie can do this. HOwever, having said that, I suspect you know that he is growling and not talking. What i would suggest is that you do educate the children, you have realised how important this is, and indeed this can have ahuge bearing on the way dogs are with the family when older.
Family contact esp. with kids is hopefully a looked forward to event, not a sort of "OMG its the kids again" concern ;)
If he growls, don't on any account put him down as he will then have got what he wanted and will quickly learn to manipulate you and the children by growling. What may be best is to plan controlled training sessions to A) show him that growling will not get him what he wants, and B) to show him that handling is pleasurable.
I would regulalry handle him gently, feel his legs, ears, tummy, stroke him all over, taking care to support him if lifted, and pop him lots of really tasty titbits during this time - liver, chicken, fresh meat or cheese - and with calm and firm handling he should get used to it, accept it and in time, start to like it. The idea is that he eventually looks forward to it!!!

When he starts to relax during the sessions, you can start to offer less titbits and gradually stop them altogether. But do keep an eye on the kids because although he will have a high pain tolerance <g>, he can still be hurt if picked up quickly in excitemetn for a cuddle, and can still be frightend if shocked into being awake when he is napping, esp. as pups do sleep so deeply.
Anyway just my thoughts, good luck.
LIndsay :)