There are a number of options for containing stuffed animals that I'm sure you have seen or considered. Depending on a child's age, number of stuffed animals, how often they use them, etc, different options are better in different situations.
For kids who have a lot of stuffed animals but don't need to see them all the time, stuffing a body pillow with them is a great way to contain these soft toys. They can be accessed through the zipper when needed, but the rest of the time they are out of the way! This reduces visual clutter and also makes the room easier to straighten up when it's time to clean up toys because the majority of the stuffed animals stay inside the pillow case(s).
Here's a picture of a project I worked on this past spring. Before we started there were stuffed animals everywhere! When we finished, we had a few favorite stuffed animals out for regular use and the rest were tucked away in pillows that created a cozy reading area. Happy parents and happy kids - I definitely call this organizing project a success!
Hope this helps you contain the zoo in your child's room!