  Let $(X,L_X)$ be a polarized manifold and $D$ be a smooth hypersurface such
that $D \in | L_X |$. In this paper, we show that if there is no nontrivial
holomorphic vector field on $D$ and ${\rm Aut}_0 ((X,L_X); D)$ is trivial, then
constant scalar curvature K\"{a}hler metrics of Poincar\'{e} type on $X
\setminus D$ can be approximated by constant scalar curvature K\"{a}hler
metrics with cone singularities of sufficiently small angle along $D$. This
result implies log K-semistability of $((X,L_X);D)$ with angle 0.
