  We construct the equation of state for high density neutron star matter at
zero temperature using the two-flavor Nambu--Jona-Lasinio (NJL) model as an
effective theory of QCD. We build nuclear matter, quark matter, and the mixed
phases from the same NJL Lagrangian, which has been used to model free and
in-medium hadrons as well as nuclear systems. A focus here is to determine if
the same coupling constants in the scalar diquark and vector meson channels,
which give a good description of nucleon structure and nuclear matter, can also
be used for the color superconducting high density quark matter phase. We find
that this is possible for the scalar diquark (pairing) interaction, but the
vector meson interaction has to be reduced so that superconducting quark matter
becomes the stable phase at high densities. We compare our equation of state
with recent phenomenological parametrizations based on generic stability
conditions for neutron stars. We find that the maximum mass of a neutron star,
with a color superconducting quark matter core, exceeds $2.01 \pm
0.04\,M_\odot$ which is the value of the recently observed massive neutron star
PSR J0348+0432. The mass-radius relation is also consistent with gravitational
wave observations (GW170817).
