Really small mounted cannon, really little more than muskets too large to be used with just hands, were AFAIK tried at several points of hitory. None, AFAIK, were worth the trouble or too effective. Taking a light field piece, reducing the weight of the frame to a minimum, and adding a larger team of horses were generally a way better method for creating genuinely mobile firepower that could keep up with cavalry.

I don't really know how much your average elephant can bear and what the requirements for frames would be, but I strongly suspect it is simply physically impossible to mount a cannon heavier than the really light close-support guns - type 2-pounder or something similarly puny - on a howdah without serious issues with weight and recoil. Mind you, especially if they're of the breech-loading variety and use something similar to grapeshot, those things aren't half bad antipersonnel weapons.