I think viscocity is independent of pressure because we will say the viscocity for water as 1*10^-3 kg/ms for whatever the pressure as like as the other fluids but it is possible if we assume that it is steady,incompressible(bulk modulus is very high) flow(not fluid).
In a similar way we can't say the density of water to be 1000kg/m3(it is possible by the above assumptions only).But it is dependent of temperature.Increase in temperature will decrease the viscocity.