The task of Sign Language Production (SLP) in machine learning involves converting text-based spoken language into corresponding sign language expressions. Sign language conveys meaning through the continuous movement of multiple articulators, including manual and non-manual channels. However, most current Transformer-based SLP models convert these multi-channel sign poses into a unified feature representation, ignoring the inherent structural correlations between channels. This paper introduces a novel approach called MCST-Transformer for skeletal sign language production. It employs multi-channel spatial attention to capture correlations across various channels within each frame, and temporal attention to learn sequential dependencies for each channel over time. Additionally, the paper explores and experiments with multiple fusion techniques to combine the spatial and temporal representations into naturalistic sign sequences. To validate the effectiveness of the proposed MCST-Transformer model and its constituent components, extensive experiments were conducted on two benchmark sign language datasets from diverse cultures. The results demonstrate that this new approach outperforms state-of-the-art models on both datasets.