Viscous damping is non-linear in nature because the force depends on the flow velocity derivatives. Thus, you could only find exact relations by solving the Navier-Stokes Equation. These relations shall be non-linear as well.

Your damping ratio must then be a function not only on the viscosity value, but also on the initial amplitude of motion, given that all other parameters remain the same, and this includes the mass density of the fluid!

However, your problem may be facilitated by considering the fluid dynamics' non-dimensionals: The drag coefficient (Cd) is the non-dimensional that relates the drag force with the parameters of your problem. Since you have an oscillatory motion, you may expect a smooth relation between the drag coefficient with the Keulegan-Carpenter number (Kc), you just need to consider the velocity parameter as 2*pi*(Amplitude of motion)/(Period) at this evaluation. The coefficients read:

Cd = (Drag force)/[0.5*(Density)*(Characteristic length)^2*(Velocity)]

Kc = (Velocity)*(Period)/(Characteristic length)

I see you have the relation between viscosity and drag force already, so I suggest you try plotting this. Then, for any modification on your problem parameters, giving that the problem remains geometrically similar, you could use the same non-dimensional plot. You could always obtain the drag force for the current Kc with this one plot.

Because of the non-linearity of the problem, your damping ratio will vary on time in the case of free decay, for instance. However, for a given expected amplitude of motion and parameters known a-prior, this shall work pretty well and encompass the different fluids you have tested.

Thank you Thiago, it was so long to read this answer, It is a direct answer I will need to do more study on it, surely I will contact very soon, again thanks