Could you explain a little more about why the plant isn't sitting upright on it's own? Is it that it's too low in in the pot? Or that it's tipping over somehow?
The container is significantly larger (especially too tall) than the potted plant. so I've put other empty pots upside down in the container, and then I sit the potted plant on top of the overturned pot, but the overturned pot has a smaller surface area than the bottom of the potted plant's plastic container. So it tips over or leans inside the outer container.
The main thing is you don't want anything that will make the smaller pot sit in a puddle of water. Most plants don't care for it.
I don't think there is anything specifically made for this, unfortunately. I think you want something that either increases the size of the 'base' the inner pot is sitting on OR something like a mini stand that holds the inner pot at the desired height. I'm thinking something like
this, but less decorative.
I would try thrift stores for cylindrical plastic objects that are cheap and you can cut up as necessary. Depending on the outer pot size, the basket from a salad spinner or a juice jug could work for the bottom section, and you could cut out the center a bit if you needed/wanted.
You could also get polymer clay from a craft store and make your own stand that is custom fit for the given pot combination! I'm thinking a ring that fits around the inner pot with legs or sides to hold it at the desired height. Note that I haven't worked with polymer clay much, so I don't know if that's the right medium, but it seems easier than woodworking or metalworking!
If you don't want to bother with finding a different system for raising the height of the inner pot, smaller cylinders like disposable water bottles could go around the edges of the inner pot to keep it centered. If you cut off the top and bottom, it will be pretty flexible and won't hold excess water to attract bugs.
If you are interested in potentially elongating your plants lives, it sounds like they might like to get more light, or possibly be fertilized once or twice a year.
Good luck! Let us know if you work something out!