  The coherent states associated to the discrete serie representations
$D(E_o,s)$ of $SO(3,2)$ are constructed in terms of (spin-)tensor fields on
$D=4$ anti-de Sitter space. For $E_o>s+5$ the linear space ${\cal H}_{E_o,s}$
spanned by these states is proved to carry the unitary irreducible
representation $D(E_o,s)$. The $SO(3,2) $-covariant generalized Fourier
transform in this space is exhibited. The quasiclassical properties of the
coherent states are analyzed. In particular, these states are shown to be
localized on the time-like geodesics of anti-de Sitter space.
