Large slabs of clay
Cover balloon with reasonably thin slabs of clay (they must be long enough that they meet around the balloon). Make sure to leave a small hole at the top, large enough to pull the once-popped balloon out.
Pinch or slightly smooth out the edges. There shouldn’t be any holes but these are not meant to look pretty or perfect.
Let the eggs dry on paper plates for a couple of days, pop the balloons and let dry for a few more weeks.
Decorate with paint. For example, some kids painted theirs like dragon eggs.
There’s a fine line between too little clay that will not hold up its weight when the balloon is popped and too much clay which will collapse on itself. Use your best judgement and good luck.