I think it would be best to provide pumpkins for the invited children (they can be small pumpkins, as long as they're suitable for carving a small design). On the invitation, you can let people know that a small pumpkin will be provided for each child, but that they are welcome to bring any additional pumpkins that they would like to carve.
I have to agree with everyone else.
I also really like the idea that a previous poster had about buying the really small pumpkins and decorating them instead of carving them.
A few people have suggested this, and I would just like to make one point here. A pumpkin painting party could be a lovely thing, but if the OP has a tradition of a pumpkin carving
party, I suspect a lot of the guests might be disappointed by the change. Pumpkin carving isn't just a way of putting a picture on a pumpkin, it's a particular art form. You have only two or three colors (peeling the skin gives the third color); you have to structure the design so that all the dark areas are connected and won't collapse (trivial for the traditional jack-o-lantern face, but very challenging for some other designs); if you scrape the pumpkin thin enough, the whole pumpkin glows and highlights the texture and ribs of the pumpkin. The technique (and the resulting aesthetic) is completely different from a painted pumpkin.