Large Language Models (LLMs) are widely applied in educational practices, such as for generating children's stories. However, the generated stories are often too difficult for children to read, and the operational cost of LLMs hinders their widespread adoption in educational settings. We used an existing expert-designed children's reading curriculum and its corresponding generated stories from GPT-4o and Llama 3.3 70B to design different experiments for fine-tuning three 8B-parameter LLMs, which then generated new English reading stories that were subjected to quantitative and qualitative evaluation. Our method prioritizes controllability over scale, enabling educators to target reading levels and error patterns with a compact, affordable model. Our evaluation results show that with appropriate fine-tuning designs, children's English reading stories generated by 8B LLMs perform better on difficulty-related metrics than those from zero-shot GPT-4o and Llama 3.3 70B, with almost no discernible safety issues. Such fine-tuned LLMs could be more broadly used by teachers, parents, and children in classrooms and at home to generate engaging English reading stories with children's interests, controllable difficulty and safety.