A hovering multirotor generates a lot of turbulance, which can result in a bumpy hover. Gimbals are great at smoothing out pitch and roll, but not vertical or lateral movements.
One option could be to turn off your altitude hold during the shot. The drone will move, yes, but instead of fighting itself to hold in position (causing a wobbly video) it is more likely to just drift, the effect being more of a smooth pan which can look better (although this is subjective and may not fit the angle you are aiming for.)
A variation on this could be to try to manually hold the altitude, or to deliberately not hold by commanding a slight climb/descent so that again the aircraft is moving, but in a smooth fashion.
A second solution is to fix it in post. If the movement isn't huge, and you can afford to lose a few pixels (say, shooting in 4K but want a HD output) you could apply image stabilisation using video editing software.
Finally, let the aircraft settle before your shot. If you need to manually press the record button, do it before you start flying the aircraft for the shot as you can then keep your hands (and the sticks) still for the duration. Reaching for the record button might cause you to accidentally command the exact wobble you're trying to minimise!
If this is the S49 you were posting about yesterday, I don’t think you will be able to stop this motion.
To maintain your position, you constantly need to pitch and roll to fight changing wind conditions.
As your drone has a fixed camera, the camera will also have to pitch and roll as well, creating the unwanted motion.
If the lifting capacity is great enough, you could probably design a light soft mount for your camera that would remove some of the more subtle oscillations. You can also use post-processing software to stabilise the footage.
Unfortunately, as far as I am aware, there is no mechanical way to stabilise your camera barring a gimbal, which will likely be too heavy for your quad to lift.
With enough practice, for example setting up a target and trying to keep it in centre frame, you may be able to compensate for the wobbling.
I'm going to assume that you don't need your videos to be stabilised realtime. In this case you need image stabilisation software.
I'm not an expert in this field particularly, so I'll copy the most relevant answers on this reddit thread.