Green's function for Laplace operator in a conformally flat metric?

Question

Given the Laplace–Beltrami operator $\nabla^2$, does there exists a closed form for the greens function $G$ such that $\nabla_x^2G(x,y)=-\delta(x,y)$, and $$ \nabla_x^2\iiint_{y^3}G(x,y)f(y)dy^3=-f(x) \ , \ $$ if we know that the metric defining $\nabla^2$ is conformally flat? $$ \nabla^2 \phi = |g|^{-1/2} \partial_\mu\left( |g|^{1/2} g^{\mu\nu} \partial_\nu\right)\phi $$