  We describe the differential graded Lie algebras governing Poisson
deformations of a holomorphic Poisson manifold and coisotropic embedded
deformations of a coisotropic holomorphic submanifold. In both cases, under
some mild additional assumption, we show that the infinitesimal first order
deformations induced by the anchor map are unobstructed. Applications include
the analog of Kodaira stability theorem for coisotropic deformation and a
generalization of McLean-Voisin's theorem about the local moduli space of
lagrangian submanifold. Finally it is shown that our construction is homotopy
equivalent to the homotopy Lie algebroid, in the cases where this is defined.
