Low-density parity-check (LDPC) codes, particularly nonbinary LDPC (NB-LDPC) codes, are essential for meeting the high peak data rate requirements of the 6th generation systems. However, challenges arise from correlated noise, caused by factors like seasonal variations and inaccuracies in signal-to-noise ratio estimation, which hinder their practical deployment. In this paper, we propose a convolutional neural network-aided iterative detection and decoding (CNN-IDD) method for NB-LDPC coded modulation systems, aiming to enhance performance over correlated noise channels with a slight increase in complexity. In this system, a convolutional neural network (CNN) is integrated with iterative hard-reliability-based algorithms to learn from the correlated noise. The CNN and the hard-decision decoder interact iteratively to mitigate noise effects and improve estimation accuracy. Simulation results show that the proposed scheme achieves up to 1 dB improvement in performance, while maintaining the low complexity advantage of traditional hard-reliability decoding for high-order modulation in NB-LDPC systems over correlated noise channels.