There is always the temporary electric fencing. Then there are corral panels. You can find smaller size ones than the big ones at TSC. Not sure what else would be easy to move.
I would never tie my goats out without supervision. Think about them getting away in case of a predator. They can also find a way to wrap themselves up in any kind of rope or chain even when there's nothing to get tangled on.
I'm thinking I may get some cattle panels for the kid playpen and move it around the yard while we're there. But again, I wouldn't leave them unsupervised.