Honeycomb structure has been frequently observed in two-dimensional (2D) materials. CuAu in the buckled honeycomb (BHC) structure has been synthesized recently, which is the first case of 2D intermetallic compounds. Here, the dynamical stability of 2D AX in the BHC structure, where A = Cu, Ag, and Au and X is a metallic element in the periodic table, is systematically studied by calculating phonon dispersions from first-principles. Among 135 AX, more than 50 AX are identified to be dynamically stable. In addition, (i) a relationship between the dynamical stability and the formation energy, (ii) a correlation of dynamical stability between different constituents A, (iii) a trend of lattice parameters, and (iv) electronic and magnetic properties are discussed. Furthermore, a stable phase of B11-type AuZr is predicted based on both the result (ii) and the stability relationship between 2D and three-dimensional structures. The present findings stimulate future studies exploring physics and chemistry of 2D intermetallic compounds.