Assume pressure (P), length (L) and velocity (V) are fundamental quantities, then the dimensions of coefficient of viscosity (η) is

Coefficient of viscosity is given by η=FA  dv/dz
Dimension of force F=[MLT⁻²]
Dimension of Area A=[L²]
Dimension of velocity gradient dv/dz=[T⁻¹]
Thus dimension of coefficient of viscosity η=[MLT⁻²] / [L²][T⁻¹]=[ML⁻¹T⁻¹]