  We show that the Bergman metric of the ball quotients $\mathbb{B}^2/\Gamma$,
where $\Gamma$ is a finite and fixed point free group, is K\"ahler-Einstein if
and only if $\Gamma$ is trivial. As a consequence, we characterize the unit
ball $\mathbb{B}^2$, among 2 dimensional Stein spaces with isolated normal
singularities, proving an algebraic version of Cheng's conjecture for 2
dimensional Stein spaces.
