Low-density parity-check (LDPC) codes, including nonbinary LDPC (NB-LDPC) codes, are essential for meeting the high peak data rate requirements of mobile communication 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 of the complexity. In this system, a CNN is integrated with iterative hard-reliability-based algorithms to learn from the correlated noise. The CNN and 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.