Ferroelectricity with out-of-plane polarization has so far been found in several two-dimensional (2D) materials, including monolayers comprising three to five planes of atoms, e.g., α-In2Se3 and MoTe2. Here, we explore the generation of out-of-plane polarization within a one-atom-thick monolayer material, namely hexagonal boron nitride. We performed density-functional-theory calculations to explore inducing ferroelectric-like distortions through incorporation of isovalent substitutional impurities that are larger than the host atoms. This disparity in bond lengths causes a buckling of the h-BN, either up or down, which amounts to a dipole with two equivalent orientations. We tested several impurities to explore the magnitude of the induced dipole and the switching energy barrier for dipole inversion. The effects of strain, dipole-dipole interactions, and vertical heterostructures with graphene are further explored. Our results suggest a highly-tunable system with ground state antiferroelectricity and metastable ferroelectricity. We expect that this work will help foster new ways to include functionality in layered 2D-material-based applications.