Parenting coaching programs have proven to be effective; however, fewer studies have explored the capabilities of AI-powered chatbots to deliver online parenting coaching programs. This paper addresses this gap by proposing the AI-Powered Parental Coaching System (APPCS), an AI chatbot designed to provide effective coaching for parents. Unlike the existing solutions, APPCS focus on continuous tracking and adaptation based on the historical interventions and reactions of parents by leveraging the abilities of Large Language Models (LLMs). This feature remains unexplored in current literature. The paper highlights the powerful capabilities of LLMs to generate compelling results through appropriate prompt engineering, even without being specifically fine-tuned for parental coaching. Finally, it presents proposed architecture for APPCS, highlighting its capabilities to support parents in enhancing communication and interaction with their children.