This should be a porous material. Depending on what stiffness is required, it can either change its own properties or be filled with gaseous or liquid media of pores to adjust resonance frequency.
A string under tension, like on bowed or plucked string instruments with variable tension. Same for a tuneable drums. A vibration insulator could in principle be a "drum" with adjustable tension, however the main tension may come from the object it supports.
Another possibility is to use a hygroscopic porous material in a container and subject it to different RH levels from given salt solutions.
Using different amounts of fluid, like water, in a porous material would also be a possibility, something we often may see outdoors. Could be utilized indoors in a container.
A more advanced method is to use a control system with controlled stiffness.
Basically you can tune the natural frequency by varying the mass and stifness of the system. Stiffness is stringly dependent in material, but also in geometry. Try to play with those parameters.
For instance, you can also put a sanple with a preload and vary that.
Depends on the application you have in mind. Sound, vibration, which fluids, etc.?
As you already excluded magnetic fields and therefore magnetorheological fluids, you might think about electrorheological materials / fluids - however, they bear their own challanges in applications (e.g. high electic field strength / high voltages).
Mechanical solutions, i.e. dynamic stiffness depending on prestress / preload have already be mentioned...
Or you might go with (semi-)active metamaterials...