Hypothetically, if you had a gas made of really heavy atoms/molecules (although it's unlikely that they would be stable at the kind of Uranium-heavy I'm thinking of, let's say that hypothetically they are) in a liquid made of really really light molecules or atoms (e.g hydrogen), and say that temperature isn't going to change the given states of the elements (very very hypothetically), and so they can exist in the states they need to together, could the bubbles go down? Or would the relative densities make the masses of the atoms and molecules irrelevant?
Under really high pressures you might be able to make bubbles of xenon or radon (don't try that one at home!) sink in liquid lithium. It is opaque however, so you would have to study their behaviour with X-rays or ultrasound or the like. But I would expect them to sink and then coalesce like any rising bubbles.
A pressure of some thirty or forty atmospheres should do it for xenon.
Hm. at pressures not much higher than that you might manage it in water.
Go up in a hot air balloon; pour a glass of fizzy lemonade; cut the ropes attaching the basket to the balloon; as you cut the last rope, quickly invert the glass; witness the bubbles going downwards; enjoy the sight for a few seconds and then deploy parachute.
Don't try it in a built-up area because the falling basket might injure someone.
Alternatively, how about putting the lemonade in a bucket and whirling it around? The bubbles should go down but they might be hard to watch.
In a simplistic way this effect can be viewed at your local pub if you pour a Guiness. The bubbles from the foamhead appear to be going down to the bottom of the glass. They seem to be behaving as waves cascading down the sides of the glass.
*note: yes they may be rising in respect to their surrounding liquid but the overall effect is bubbles going down, which is quite fun to watch!