As large language models (LLMs) are widely adopted, new safety issues and policies emerge, to which existing safety classifiers do not generalize well. If we have only observed a few examples of violations of a new safety rule, how can we build a classifier to detect violations? In this paper, we study the novel setting of domain-generalized few-shot learning for LLM-based text safety classifiers. Unlike prior few-shot work, these new safety issues can be hard to uncover and we do not get to choose the few examples. We demonstrate that existing few-shot techniques do not perform well in this setting, and rather we propose to do parameter-efficient fine-tuning (PEFT) combined with augmenting training data based on similar examples in prior existing rules. We empirically show that our approach of similarity-based data-augmentation + prompt-tuning (DAPT) consistently outperforms baselines that either do not rely on data augmentation or on PEFT by 7-17% F1 score in the Social Chemistry moral judgement and 9-13% AUC in the Toxicity detection tasks, even when the new rule is loosely correlated with existing ones.