Climate downscaling bridges the gap between coarse-resolution General Circulation Model (GCM) outputs and the fine-resolution data needed for regional assessments. Traditional dynamic and statistical downscaling methods face limitations in computational efficiency and accuracy. Leveraging recent advancements in deep learning, particularly convolutional neural networks (CNNs), we propose an improved method for downscaling coastal sea surface temperature (SST). Our approach introduces a novel composite loss function combining Mean Squared Error with perceptual loss, effectively capturing the high seasonal variations typically in the coastal zones. Additionally, we redesign the YNet CNN to incorporate historical monthly mean SST, enhancing its performance. Comprehensive experiments using real-world SST GCM data and observational monthly SST data show our method significantly outperforms existing techniques in coastal zones up to 50 km offshore. Case studies in New Zealand further demonstrate the reduced errors achieved by our method.