This paper proposes a coordinated beamforming scheme for a multi-cell integrated sensing and communication (ISAC) system. A target-centric graph is constructed, with the coordinate system centered at the detection target. Specifically, base stations (BSs) and users are represented as nodes, with their coordinates serving as node features, while channel realizations between nodes are modeled as edge features. To evaluate sensing performance, the Neyman-Pearson detector is employed to compute the detection probability for a fixed false alarm probability. The optimization problem is formulated to maximize the detection probability of the target at the origin while ensuring QoS communication requirements and satisfying the transmit power budget. This sensing-centric problem is addressed using graph neural networks (GNNs), which generate parameterized policies for coordinated beamforming. The GNNs are trained via primal-dual approach, leveraging a small duality gap for efficient convergence. Additionally, specific layers are utilized to generate user association policies for communication links, enabling efficient processing of the graph-structured data after sparsity enhancement. Simulation results validate the feasibility and effectiveness of the proposed GNN-based approach in achieving high detection probability.