  We investigate Cox rings of symplectic resolutions of quotients of
$\mathbb{C}^{2n}$ by finite symplectic group actions. We propose a finite
generating set of the Cox ring of a symplectic resolution and prove that under
a condition concerning monomial valuations it is sufficient. Also, three
4-dimensional examples are described in detail. Generators of the (expected)
Cox rings of symplectic resolutions are computed and in one case a resolution
is constructed as a GIT quotient of the spectrum of the Cox ring.
