  We obtain upper bounds for the rates of convergence for the simple random
walk Green's function in the domains $D_\alpha =
D_{\alpha}(n)=\{re^{i\theta}\in \mathbb{C}:0 <\theta<2\pi-\alpha,
0<r<2n\}-z_0,$ where $z_0\in\mathbb{Z}^2$ is a point closest to
$ne^{i(\pi-\alpha/2)}$. The rate depends on the angle of the wedge and is what
was suggested by the sharpest available results in the extreme cases $\alpha
=0$ and $\alpha=\pi$. Our proof uses the KMT coupling between random walk and
Brownian motion.
