Large language models (LLMs) have shown promise in many natural language understanding tasks, including content moderation. However, these models can be expensive to query in real-time and do not allow for a community-specific approach to content moderation. To address these challenges, we explore the use of open-source small language models (SLMs) for community-specific content moderation tasks. We fine-tune and evaluate SLMs (less than 15B parameters) by comparing their performance against much larger open- and closed-sourced models in both a zero-shot and few-shot setting. Using 150K comments from 15 popular Reddit communities, we find that SLMs outperform zero-shot LLMs at content moderation -- 11.5% higher accuracy and 25.7% higher recall on average across all communities. Moreover, few-shot in-context learning leads to only a marginal increase in the performance of LLMs, still lacking compared to SLMs. We further show the promise of cross-community content moderation, which has implications for new communities and the development of cross-platform moderation techniques. Finally, we outline directions for future work on language model based content moderation. Code and models can be found at https://github.com/AGoyal0512/SLM-Mod.