Scene graphs capture complex relationships among objects, serving as strong priors for content generation and manipulation. Yet, reasonably manipulating scene graphs -- whether by adding nodes or modifying edges -- remains a challenging and untouched task. Tasks such as adding a node to the graph or reasoning about a node's relationships with all others are computationally intractable, as even a single edge modification can trigger conflicts due to the intricate interdependencies within the graph. To address these challenges, we introduce SG-Tailor, an autoregressive model that predicts the conflict-free relationship between any two nodes. SG-Tailor not only infers inter-object relationships, including generating commonsense edges for newly added nodes but also resolves conflicts arising from edge modifications to produce coherent, manipulated graphs for downstream tasks. For node addition, the model queries the target node and other nodes from the graph to predict the appropriate relationships. For edge modification, SG-Tailor employs a Cut-And-Stitch strategy to solve the conflicts and globally adjust the graph. Extensive experiments demonstrate that SG-Tailor outperforms competing methods by a large margin and can be seamlessly integrated as a plug-in module for scene generation and robotic manipulation tasks.