In the frame of the discrete dipole approximation, the propagation of magnons in quasi-one-dimensional resonant structures made of nanometric magnetic clusters is examined theoretically. These resonant structures, composed of a nanometric magnetic cluster chain and adsorbed clusters near the chain, may exhibit sharp peaks (dips) in the magnon transmission spectrum. Stop bands and sharp resonant magnonic states in the gaps can be created with an appropriate choice of the geometrical or magnetic parameters of the structure. These resonant states result from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or placed between two zeros of transmission. This model may have potential applications in constructing magnon filter devices.