  We perform a Fisher matrix analysis to forecast the capability of ongoing and
future Sunyaev-Zeldovich cluster surveys in constraining the deviations from
Gaussian distribution of primordial density perturbations. We use the
constraining power of the cluster number counts and clustering properties to
forecast limits on the $\fnl$ parameter. The primordial non-Gaussianity effects
on the mass function and halo bias are considered. We adopt self-calibration
for the mass-observable scaling relation, and evaluate constraints for the SPT,
Planck, CCAT--like, SPTPol and ACTPol surveys. We show that the
scale-dependence of halo bias induced by the local NG provides strong
constraints on $\fnl$, while the results from number count are two orders of
magnitude worse. When combining information from number counts and power
spectrum, the \planck\ cluster catalog provides the tightest constraint with
$\sigma_{\fnl}=7$ (68% C.L.) even for relatively conservative assumptions on
the expected cluster yields and systematics. This value is a factor of 2
smaller than the $1\sigma$ error as measured by WMAP CMB measurements, and
comparable to what expected from Planck. We find that the results are mildly
sensitive to the mass threshold of the surveys, but strongly depend on the
survey coverage: a full-sky survey like Planck is more favorable because it can
probe longer wavelengths modes which are most sensitive to NG effects. In
addition, the constraints are largely insensitive to priors on nuisance
parameters as they are mainly driven by the power spectrum probe which has a
mild dependence on the mass-observable relations.
