Unstable, shaky, wobbly, rickety, precarious, unreliable: these are all antonyms for the phrase "stable stand". When we speak of a stable stand, we usually mean something that is securely planted or set in place, something that won't topple over or collapse. The opposite of that, then, is something that is unsteady or unsafe. A wobbly stand might be okay for a small bookshelf, but it wouldn't work for supporting a heavy piece of machinery. So, when considering what antonyms to use for "stable stand", it depends on the context and the degree to which you're trying to emphasize the lack of stability.