Humor generation poses a significant challenge for Large Language Models (LLMs), because their standard training objective (next-token prediction) inherently conflicts with the surprise and incongruity required for comedy. To bridge this gap, we introduce the Cognitive Synergy Framework, a methodology for generating highquality humor data inspired by psychological theories of humor. Utilizing a Mixtureof-Thought (MoT) approach, we deploy six cognitive personas (e.g., The Absurdist, The Cynic) to synthesize diverse comedic perspectives for a given prompt. This framework produces a theory-grounded dataset, which we use to fine-tune a 7B-parameter student model. We further evaluate two alignment strategies, Direct Preference Optimization (DPO) and an offline group-relative variant O-GRPO, finding that neither improves over SFT. However, our 7B HumorGen model variants significantly outperform larger instruction-tuned baselines and achieve top-tier open-weight performance while remaining competitive with frontier proprietary systems. These results suggest that cognitively driven data curation is more critical than alignment algorithms or model scale for humor generation.