Aiming at the demodulation technology of coherent OAM multiplexed beam in OAM communication system, an amplitude-only diffractive deep neural network (D2NN)-based implementation method for OAM coherent multiplexing is proposed. The performance of the demodulator is investigated via numerical experiments and characterized by the bit error rate (BER). An advanced OAM selection strategy is proposed to reduce the BER of D2NN. And compared with the phase-only D2NN demodulator, simulation experiments verify that the amplitude-only D2NN has obvious advantages in high demultiplexing and demodulation accuracy for quad-OAM coherently multiplexed beam, which provides a flexible robust real-time demodulation approach for OAM coherent multiplexing communication.