I wadded up some newspaper, put it next to the balloon (I did try to tape it but the dried paste refused), and wrapped it in tissue paper. I think this method could work for any shape. As a bonus children shall be pelted with wadded up newspaper balls when the pinata is hit. With hindsight I should have made the newspaper balls look like little baby birds so it would be like the children are getting attacked.
It actually looks like an angry bird to me. Well an angry bird rip-off. Which is exactly what this is.
Instead of filling the pinata with eggs, I found a bunch of tiny toys at the thrift store. There are some genuine micro machines in there for the 80's kids' kids. And some wee power rangers for the 90's kids' kids.