Causal inference is a crucial task in natural language understanding, aiming to determine causal relationships between texts. Causal discovery (CD), a core subtask, requires not only contextual comprehension but also reliable and domain-specific knowledge to judge whether a causal relation exists between two sentences. However, existing methods often rely on external knowledge retrieval, which may be contextually misaligned or fail to cover relevant information, limiting their effectiveness. To address these challenges, we propose Causal Inference Supervised Directed Knowledge Generation (CISDKG), a novel framework that generates knowledge that is both contextually rich and reliable. Knowledge from large teacher models is first classified into distinct types to guide a lightweight student model for directed knowledge generation. We further introduce a Causality-based Knowledge Effectiveness Score (CKES) to evaluate the relevance and authenticity of generated knowledge, enabling effective filtering of spurious information. Moreover, a soft-prompt tuning strategy enhances the diversity and specificity of knowledge conditioned on these types. The generated knowledge benefits causal inference, while feedback from the reasoning process refines knowledge filtering, forming a collaborative loop that improves both knowledge quality and CD performance. Experiments on public benchmarks show that CISDKG produces contextually aligned knowledge and achieves superior performance over existing approaches.