This paper proposes an audio-data hiding scheme for amplitude-modulation (AM) radio broadcasting systems. The digital-audio method of watermarking based on cochlear delay (CD) that we previously proposed is employed in this scheme to send an inaudible message. We investigate the feasibility of a data-hiding scheme in the AM domain by applying the method of CD-based inaudible watermarking. The proposed scheme embeds both original and watermarked signals as lower and upper sidebands into the AM signals by using the method of double-sideband with carrier (DSB-WC) and then transmits them to the receivers. Particular receivers in the proposed scheme can detect both original and watermarked signals by demodulating both sidebands with DSB-WC and then extract messages from the watermarked signal with the original signal using CD-based watermarking. The results we obtained from computer simulations revealed that the proposed scheme can transmit messages as watermarks in AM radio systems and then correctly extract the messages from AM signals. The results also indicated that the sound quality of the demodulated signals could be kept at higher levels not only with the proposed scheme but also in traditional AM radio systems. This means that the proposed scheme has the possibility of acting as a hidden-message transmitter as well as having low-level compatibility in AM radio systems.