This paper studies the constellation diagram design for a class of communication systems known as near-field direct antenna modulation (NFDAM) systems. The modulation is carried out in a NFDAM system by means of a control unit that switches among a number of pre-designed passive controllers such that each controller generates a desired voltage signal at the far field. To find an optimal number of signals that can be transmitted and demodulated reliably in a NFDAM system, the coverage area of the signal at the far field should be identified. It is shown that this coverage area is a planar convex region in general and simply a circle in the case when no constraints are imposed on the input impedance of the antenna and the voltage received at the far field. A convex optimization method is then proposed to find a polygon that is able to approximate the coverage area of the signal constellation diagram satisfactorily. A similar analysis is provided for the identification of the coverage area of the antenna input impedance, which is beneficial for designing an energy-efficient NFDAM system.