How to modify viscosity of ZnO ink?
Regular black ink is pretty viscous it has a dynamic viscosity ($\eta$) of 4.177.

In comparison a 50% mixture of methanol and glycerol has a viscosity of 5.8

Some other solvents to consider are 


Hexanol which has a viscosity of about 5.4 
Heptanol which has as viscosity of
about 7.3


These long-chain alcohols, however, will not dissolve significantly in water. 

Some more viscosity data can be found here (it's not an ideal place for viscosities but it is free)

Linseed oil is also not water soluble. In any case here is another link 

Ultimately it seems like you'd need to try a few different mixtures to get desired viscosity, solubility and evaporation speed.