Acquiring animal images with annotated identities is hard and expensive, leading to challenges in training animal individual identification models due to limited annotated data. Despite the promising advances in face image generation for face recognition and in subject-driven text-to-image diffusion models, synthesizing images of specific animal individuals with rich intra-class variations is still an open issue. In this paper, we take an animal image as being composed of general species features, distinctive individual features, and context features, and then propose a novel method to fine-tune text-to-image diffusion models that can more effectively deal with the three feature components. This is fulfilled by our proposed novel identity-preserving loss and technique of explicitly injecting identity and context features into the fine-tuning process. We apply our method for generating images of individual red pandas and giant pandas, and prove the utility of the generated synthetic images in augmenting the training data of identification models on two benchmarks.