From an engineering and practical point of view, very good models have been proposed.
For temperature dependency, Vogel proposed $$\Large\eta=a~ e^{\frac{b}{T+c}}$$ (ignore $c$ if you want to have a model which can be linearized to provide you good estimates for the nonlinera regression - but, in such a case, $T$ must be absolute) and for pressure dependency, Barus proposed $$\Large\eta=\eta_0~ e^{\alpha P}$$
If I had to solve your problem, I should work independently each isobar in order to get for each pressure the value of the coefficients $a,b,(c)$. Then, plot each of the parameters as a function of pressure to see if something even simpler could be emprically found. If not, for the considered temperature, compute the viscosity at the different pressures and just interpolate linearly.
If I may add a comment : very few (or even less) physical properties are represented by polynomials.
Added later to this answer
Searching my old notes, I found that I used (very long time ago), a model which write $$\Large\eta=\eta_0 \exp \left(\frac{{c_1} (T-T_0)}{{c_2}+(T-T_0)}+ [d_1 +d_2
(T-T_0)]~(P-P_0)\right)$$ which was quite good. You can see that it is just a combination of the other models with a simple assumption concerning the dependency of parameter $\alpha$ with respet to temperature.
Added later to this answer
In order to make your life simple, you could consider as a model $$\Large\eta=e^{a+b P +\frac{c+dP}{T}}$$ So $$\log(\eta)={a+b P +\frac{c+dP}{T}}$$ So perform a linear regression with independent variables $P,\frac{1}{T},\frac{P}{T}$; this gives you good estimates of the parameters $a,b,c,d$. You can now start a nonlinear regression.
