Low-frequency periodic requests are common in cloud-based enterprise applications. These infrequent requests often leave microservices idle for extended periods, leading to low resource utilization. Furthermore, the randomness of response times may decrease the reliability of the cloud platform. Intuitively, the periodic nature of requests allows for the agile deployment of microservices to promptly free up occupied computing resources. Thus, the key lies in designing low-cost, high-reliability microservice deployment schemes. Traditional approaches relying on specialized expertise are impractical because of intricate interdependencies within microservice frameworks. To address this, the Microservice Deployment Problem for Low-frequency Periodic Requests (MDP-LPR) is formulated, and a Mixed Integer Programming (MIP) model is developed. A deployment framework leveraging statistical analysis and Monte Carlo simulation is proposed to ensure high reliability. Furthermore, a two-stage heuristic algorithm named Relaxation and Precision Mixed Algorithm (RPMA) is introduced to generate low-cost deployment schemes. Finally, experiments are conducted on real-world workflows. The results show that the RPMA outperforms its counterparts in generating low-cost deployment schemes, and the proposed deployment framework enables the automatic acquisition of low-cost, high-reliability deployment schemes.