  This paper is devoted to the formulation of Self-Consistent Green's Function
(SCGF) in an explicit Nambu-covariant fashion for applications to many-body
systems at non-zero temperature in symmetry-broken phases. This is achieved by
extending the Nambu-covariant formulation of perturbation theory, presented in
the first part of this work, to non-perturbative schemes based on
self-consistently dressed propagators and vertices. We work out in detail the
self-consistent ladder approximation, motivated by a trade-off between
numerical complexity and many-body phenomenology. Taking a complex general
Hartree-Fock-Bogoliubov (HFB) propagator as the starting point, we also
formulate and prove a sufficient condition on the stability of the HFB
self-energy to ensure the convergence of the initial series of ladders at any
energy. The self-consistent ladder approximation is written purely in terms of
spectral functions and the resulting set of equations, when expressed in terms
of Nambu tensors, are remarkably similar to those in the symmetry-conserving
case. This puts the application of the self-consistent ladder approximation to
symmetry-broken phases of infinite nuclear matter within reach.
