I eventually figured that out. I thought of a whole bunch of stuff that I could use, and came up with paper machie...
Step 1: Make the Paper Machie Eye
Here's how I make paper machie glue:
1- Get some sort of plastic container. I like using the quart size Chinese restaurant soup containers. I have them lying around the house, and they are disposable, so who cares if you're filling them with glue and paper.
2- Get some flour. It doesn't matter if it's bleached or unbleached at this point, but later on when doing the final steps I would recommend using bleached flour, so why not use it all the way through? Put a few spoonfulls into the container. The exact amount really doesn't matter. On average, I put 3-4 scoops into a quart size container.
3- Add some salt to the flour. I read that it keeps the bugs from eating the flour in you paper machie, so I'm going with adding salt. Again, the exact amount doesn't matter. I use a lot less salt than flour in the mixture.
4- Add water. Normal tap water will do. Fill it up to the top of the container and mix well. You want the clumps of flour to be broken up while you mixing, and sometimes that takes some work on the first mix.
And there you have it, paper machie glue. Now take whatever kind of paper scraps you can find and rip them up into strips. Old newspapers, junk mail, Christmas catalogs, it all works. Dip the strips one at a time into the well mixed glue. Crumple them up while submerged to get all of the paper's fibers well soaked. Then remove the paper from the glue and rub off any flour that didn't get mixed properly (you'll have this problem at first, but as you do more and more, the flour will get mixed better and better). Take the glue covered paper and stick it on the balloon. Repeat this until the top half of the balloon is covered. Then do another layer of paper. I like alternating between two different types of paper so I know where I covered and where I didn't on each layer. Do three layers of paper and let the balloon dry overnight. Then do three more layers and eye dry for a few days. In this time, the balloon will probably deflate, and that's a good thing. That means all you will have is the paper machie eye. If it doesn't deflate, pop the balloon once fully dry.
Then move on to the next step...