Why not send a cookie invitation, instead of a card, or send out cookie notices for baby announcements, there are so many ways to be more creative. For my daughter's idol party, I made CD cookies and sent them to school with my daughter. Thankfully I wrote all party relevant infos onto the CD covers, because about half the cookies did not make it to the parent's house, BUT the kids were happy and totally excited, before the party even began.
How about an edible domino game? All the kids would join in, even those, who do not like games.
Another way to give presents, for example money towards a new camera, is to place the money into the bottom of the box and place an edible camera on top.
Edible medals for a bowling or sports party, which kid would not appreciate that?
Moving? How about a moving truck with the new destination on the side, or a for rent sign (vacancy sign)