How do I reduce the camera shaking when looking around?

I am working on a game that uses the phone's gyroscope to look around and I need to be able to use some sort of image stabilization when the user is looking at a specific game object. The script need to only interact with the camera and not the gyroscope script. I've tried various things like Quaternion.RotateTowards() and Quaternion.Lerp(), but they don't seem to do the task I need. Any guidance on this would be greatly appreciated. Thanks in advance.