  The effect of a stochastic background of cosmological perturbations on the
luminosity-redshift relation is computed to second order through a recently
proposed covariant and gauge-invariant light-cone averaging procedure. The
resulting expressions are free from both ultraviolet and infrared divergences,
implying that such perturbations cannot mimic a sizable fraction of dark
energy. Different averages are estimated and depend on the particular function
of the luminosity distance being averaged. The energy flux, being minimally
affected by perturbations at large z, is proposed as the best choice for
precision estimates of dark-energy parameters. Nonetheless, its irreducible
(stochastic) variance induces statistical errors on \Omega_{\Lambda}(z)
typically lying in the few-percent range.
