In recent years, graph neural networks (GNNs) have been commonly utilized for social recommendation systems. However, real-world scenarios often present challenges related to user privacy and business constraints, inhibiting direct access to valuable social information from other platforms. While many existing methods have tackled matrix factorization-based social recommendations without direct social data access, developing GNN-based federated social recommendation models under similar conditions remains largely unexplored. To address this issue, we propose a novel vertical federated social recommendation method leveraging privacy-preserving two-party graph convolution networks (P4GCN) to enhance recommendation accuracy without requiring direct access to sensitive social information. First, we introduce a Sandwich-Encryption module to ensure comprehensive data privacy during the collaborative computing process. Second, we provide a thorough theoretical analysis of the privacy guarantees, considering the participation of both curious and honest parties. Extensive experiments on four real-world datasets demonstrate that P4GCN outperforms state-of-the-art methods in terms of recommendation accuracy.