  While luminosity distances from Type Ia supernovae (SNe) provide a powerful
probe of cosmological parameters, the accuracy with which these distances can
be measured is limited by cosmic magnification due to gravitational lensing by
the intervening large-scale structure. Spatial clustering of foreground mass
fluctuations leads to correlated errors in distance estimates from SNe. By
including the full covariance matrix of supernova distance measurements, we
show that a future survey covering more than a few square degrees on the sky,
and assuming a total of ~2000 SNe, will be largely unaffected by covariance
noise. ``Pencil beam'' surveys with small fields of view, however, will be
prone to the lensing covariance, leading to potentially significant
degradations in cosmological parameter estimates. For a survey with 30 arcmin
mean separation between SNe, lensing covariance leads to a ~45% increase in the
expected errors in dark energy parameters compared to fully neglecting lensing,
and a ~20% increase compared to including just the lensing variance. Given that
the lensing covariance is cosmology dependent and cannot be mapped out
sufficiently accurately with direct weak lensing observations, surveys with
small mean SN separation must incorporate the effects of lensing covariance,
including its dependence on the cosmological parameters.
