  Previously a many-body coherent potential approximation (CPA) was used to
study the double exchange (DE) model with quantum local spins S, both for S=1/2
and for general S in the paramagnetic state. This approximation, exact in the
atomic limit, was considered to be a many-body extension of Kubo's one-electron
dynamical CPA for the DE model. We now extend our CPA treatment to the case of
general S and spin polarization. We show that Kubo's one-electron CPA is always
recovered in the empty-band limit and that our CPA is equivalent to dynamical
mean field theory in the classical spin limit. We then solve our CPA equations
self-consistently to obtain the static magnetic susceptibility chi in the
strong-coupling limit. As in the case of the CPA for the Hubbard model we find
unphysical behaviour in chi at half-filling and no magnetic transition for any
finite S. We identify the reason for this failure of our approximation and
propose a modification which gives the correct Curie-law behaviour of chi at
half-filling and a transition to ferromagnetism for all S.
