Find the coefficient of an AR-model
Given that you know the autocorrelation function, you can use the Yule-Walker equations for a generic AR model of order $p$. As you are interested in the case $p=2$, there's no need to complicate things that much.

As stated in this paper, the equations for the case of an AR(2) are given by:

$$a=\frac{r_1(1-r_2)}{1-r_1^2}$$

$$b=\frac{r_2-r_1^2}{1-r_1^2}$$

where $r_i$ are the coefficients corresponding to the autocorrelation function.