For a damped simple harmonic oscillator, the damping term is linear with the velocity - and the constant of proportionality includes the viscosity of the damping medium.
If the equation of motion is
$$m \ddot{x} + 2 \zeta \omega_0 \dot{x} + \omega^2x = 0 $$
In this equation, $\zeta$ is proportional to viscosity (and contains other terms related to the geometry and surface properties).
The Q is given by
$$Q = \frac{1}{2\zeta}$$
So Q is inversely proportional to viscosity - double the viscosity and Q halves. In an equation, if you have $Q_1$ and you want $Q_2$, then you change the viscosity $\eta$ according to
$$\eta_2 = \eta_1 \frac{Q_1}{Q_2}$$
If you change the regime of the flow (laminar to turbulent, for example) then the above doesn't hold any more. It will also give you trouble if the "memory" of the liquid is long compared to the period of oscillation (in other words, if motion of your system is causing the liquid to start rotating, and it continues to rotate when your disc stops spinning, then you will find the equations will be more complex. I'm not sure I can analyze that - certainly not without some deeper thought.)