Spacecraft Pose Estimation (SPE) is a fundamental capability for autonomous space operations such as rendezvous, docking, and in-orbit servicing. Hybrid pipelines that combine object detection, keypoint regression, and Perspective-n-Point (PnP) solvers have recently achieved strong results on synthetic datasets, yet their performance deteriorates sharply on real or lab-generated imagery due to the persistent synthetic-to-real domain gap. Existing unsupervised domain adaptation approaches aim to mitigate this issue but often underperform when a modest number of labeled target samples are available. In this work, we propose the first Supervised Domain Adaptation (SDA) framework tailored for SPE keypoint regression. Building on the Learning Invariant Representation and Risk (LIRR) paradigm, our method jointly optimizes domain-invariant representations and task-specific risk using both labeled synthetic and limited labeled real data, thereby reducing generalization error under domain shift. Extensive experiments on the SPEED+ benchmark demonstrate that our approach consistently outperforms source-only, fine-tuning, and oracle baselines. Notably, with only 5% labeled target data, our method matches or surpasses oracle performance trained on larger fractions of labeled data. The framework is lightweight, backbone-agnostic, and computationally efficient, offering a practical pathway toward robust and deployable spacecraft pose estimation in real-world space environments.