Cognitive Behavioral Therapy (CBT) is a well-established, evidence-based treatment for Major Depressive Disorder. Unfortunately, there exist significant barriers to individuals accessing CBT, including cost, scarcity of therapists and stigma. This study explores the feasibility of fine-tuning small open weight large language models (LLMs) to deliver CBT for depression. Using synthetic CBT transcripts generated by the Nous Research fine-tune of Llama 3.1 405b, we fine-tuned three models: Mistral 7b v0.3, Qwen 2.5 7b, and Llama 3.1 8b. CBT fidelity was evaluated through a modified Cognitive Therapy Rating Scale (CTRS). All fine-tuned models were compared against each other, as well as their instruct-tuned variants. Simulated patient transcripts were generated for the purpose of evaluating model performance, with the instruct and CBT-tuned models acting as the therapist and DeepSeek-V2.5 acting as the patient. These simulated transcripts were evaluated on a modified CTRS by Gemini 1.5 Pro-002. Our findings demonstrated that the CBT-tuned models significantly outperformed their instruct-tuned counterparts, with an average improvement of 11.33 points (p < 0.001) on total CTRS score. Llama 3.1 8b had the strongest performance (mean CTRS score 67.86 +/- 7.24), followed by Qwen 2.5 7b (64.28 +/- 9.55) and Mistral 7b v0.3 (64.17 +/- 9.79), with these differences between models being statistically significant. The CBT-tuned models were competent in implementing core CBT techniques and providing empathetic responses, however, there were limitations observed in agenda adherence, exploration depth and long-context coherence. This study establishes that CBT specific fine-tuning can effectively encode therapeutic competencies in small LLMs, though significant technical and ethical considerations must be resolved prior to clinical deployment.