  The power spectrum of density fluctuations is a foundational source of
cosmological information. Precision cosmological probes targeted primarily at
investigations of dark energy require accurate theoretical determinations of
the power spectrum in the nonlinear regime. To exploit the observational power
of future cosmological surveys, accuracy demands on the theory are at the one
percent level or better. Numerical simulations are currently the only way to
produce sufficiently error-controlled predictions for the power spectrum. The
very high computational cost of (precision) N-body simulations is a major
obstacle to obtaining predictions in the nonlinear regime, while scanning over
cosmological parameters. Near-future observations, however, are likely to
provide a meaningful constraint only on constant dark energy equation of state
'wCDM' cosmologies. In this paper we demonstrate that a limited set of only 37
cosmological models -- the "Coyote Universe" suite -- can be used to predict
the nonlinear matter power spectrum at the required accuracy over a prior
parameter range set by cosmic microwave background observations. This paper is
the second in a series of three, with the final aim to provide a high-accuracy
prediction scheme for the nonlinear matter power spectrum for wCDM cosmologies.
