Recent advances in appearance-based models have shown improved eye tracking performance in difficult scenarios like occlusion due to eyelashes, eyelids or camera placement, and environmental reflections on the cornea and glasses. The key reason for the improvement is the accurate and robust identification of eye parts (pupil, iris, and sclera regions). The improved accuracy often comes at the cost of labeling an enormous dataset, which is complex and time-consuming. This work presents two semi-supervised learning frameworks to identify eye-parts by taking advantage of unlabeled images where labeled datasets are scarce. With these frameworks, leveraging the domain-specific augmentation and novel spatially varying transformations for image segmentation, we show improved performance on various test cases with limited labeled samples. For instance, for a model trained on just 4 and 48 labeled images, these frameworks improved by at least 4.7% and 0.4% respectively, in segmentation performance over the baseline model, which is trained only with the labeled dataset.