I think it is good to understand what viscousity and polarity mean in order to answer your question. A viscous liquid is a liquid that flows very slowly; this means that its molecules are kept together by strong forces. This happens when you are dealing with very long chain molecules such as long chain hydrocarbons.Since hydrocarbons are generally formed by carbon and hydrogen atoms, and since their bonds are non-polar (electronegativity between C and H is small), then any long chain hydrocarbon can be tried as viscous non-polar solvent.
you asked about viscous non-polar solvent. In general viscosity of a solvent increasing with density increase.So you can choose high density solvent. Here I am giving some common solvents data this may useful to you.
I suggest something like, ParaFILM (that stuff we use in the lab) is a very viscous paraffin, you can melt it... Mix it with other waxes and you get cP that you want.