The flower pots that I use are very non-tippy - small base, which is up, and broad top, which is down. I can definitely see Homers and cat litter containers as being very tippy!I'm thinking a typical "homer" (THD bucket) can easily topple over as they are light weight especially when flying down.
We use logs and cinder blocks. The blocks are not attractive, but definitely effective. One hen likes to stand on it as the concrete is cool.
I wish I had good access to sliced up trunks. I could do a lot with them in the run.