  We place constraints on the average density (Omega_m) and clustering
amplitude (sigma_8) of matter using a combination of two measurements from the
Sloan Digital Sky Survey: the galaxy two-point correlation function, w_p, and
the mass-to-galaxy-number ratio within galaxy clusters, M/N, analogous to
cluster M/L ratios. Our w_p measurements are obtained from DR7 while the sample
of clusters is the maxBCG sample, with cluster masses derived from weak
gravitational lensing. We construct non-linear galaxy bias models using the
Halo Occupation Distribution (HOD) to fit both w_p and M/N for different
cosmological parameters. HOD models that match the same two-point clustering
predict different numbers of galaxies in massive halos when Omega_m or sigma_8
is varied, thereby breaking the degeneracy between cosmology and bias. We
demonstrate that this technique yields constraints that are consistent and
competitive with current results from cluster abundance studies, even though
this technique does not use abundance information. Using w_p and M/N alone, we
find Omega_m^0.5*sigma_8=0.465+/-0.026, with individual constraints of
Omega_m=0.29+/-0.03 and sigma_8=0.85+/-0.06. Combined with current CMB data,
these constraints are Omega_m=0.290+/-0.016 and sigma_8=0.826+/-0.020. All
errors are 1-sigma. The systematic uncertainties that the M/N technique are
most sensitive to are the amplitude of the bias function of dark matter halos
and the possibility of redshift evolution between the SDSS Main sample and the
maxBCG sample. Our derived constraints are insensitive to the current level of
uncertainties in the halo mass function and in the mass-richness relation of
clusters and its scatter, making the M/N technique complementary to cluster
abundances as a method for constraining cosmology with future galaxy surveys.
