Stage has some support for built-in controllers. There is a randomly-wandering controller included. You can use this to create moving obstacles by adding additional robots that are controlled by the wander controller (or your own controller, if you want a different type of motion).
http://wiki.ros.org/stage/Tutorials/I...
If you can't use the inbuilt wander controller, an alternative is to add multiple robots to stage and control them using a ROS node that makes them wander in the way you want. This github repository has samples for using multiple robots in Stage.
https://github.com/gergia/multiple_tu...
Your wander node could either use a map and the navigation stack to randomly set goals (like this old package, or it could be a simple ranger-based movement that moves randomly while not running into things.