Let $G$ be a connected semisimple Lie group with finite center, and let $\pi$ be an integrable discrete series representation of $G$. Miličić showed that the Poincaré series of $K$-finite matrix coefficients of $\pi$, constructed with respect to a discrete subgroup $\Gamma$ of $G$, span a dense subspace of the $\pi$-isotypic component of $L^2(\Gamma\backslash G)$. Extending the analytical framework introduced by Muić, we study the inner product and non-vanishing properties of these Poincaré series, along with applications to various families of modular and automorphic forms.