Q:

How does the viscosity of the liquid in a wine glass affect its resonance?

I believe the title is self explanatory. 
How does it affect for instance the resonant frequency of the wine glass?

A:

I think that you may find this similar question of interest. 
The frequency of oscillation is determined by the equation: 
$$f = 2\pi \sqrt{\frac{k}{m}} $$
Where $k$ is the spring constant and $m$ is the mass. The spring constant of a material is a value that increases with 'stiffness' or rigidity. The more inflexible the material, the higher the value, the more flexible the material, the lower the value.
As a quick google search yields, the addition of corn syrup to water caused the frequency to decrease:

(source: k12.or.us) 
http://tuhsphysics.ttsd.k12.or.us/Research/IB12/AlbeKastGard/index.htm
This makes sense. A denser material would obviously increase the mass. Furthermore, a more viscous material would impede the oscillation of the glass. Since viscous materials are usually denser that less viscous materials, it follows that higher viscosity fluids would resonate at lower frequencies. 
Furthermore, in terms of sound waves specifically, the speed of sound through a material is reflected by the frequency it resonates at. Simple equations exist for calculating the resonance within tubes of uniform density. Wine glasses are not as simple, but the relationship holds. The slower sound moves through a material, the lower it's resonance frequency.
Having said all of this, there is probably a point where the tones will stop sounding lower and start sounding higher. This is because, at one point, the resonant frequency will become too low to be audible. At this point, the first audible resonant frequency will be the second harmonic (2x the resonant). This probably won't happen with wine glasses, but if it does, you'll know why.

