Even the smallest of memory cards should be able to easily hold the save data for at least ten different games. If at any time a game's progress can't be saved, the Wii should notify you that whatever you're putting save data into is lacking space. In the case this occurs, the Wii will absolutely never overwrite the progress of another game, you have to do that manually yourself.
In short, you've got no need to worry about your kid's progress being deleted. Happy gaming, John!