A reliable wireless sensor network (WSN) is defined as a network that functions satisfactorily, in terms of both its coverage and connectivity to the sink(s), throughout its intended mission time. Deploying reliable WSNs is especially important for critical Internet of Things (IoT) applications, such as industrial, structural health-monitoring, and military applications. In such applications, failure of the WSN to carry out its required tasks can have serious effects, and hence, cannot be tolerated. However, the deployment of reliable WSNs is a challenging problem. This is primarily attributed to the fact that sensor nodes are subject to random failures due to different factors, such as hardware failures, battery depletion, harsh environmental conditions, and so on. In this paper, the problem of deploying a WSN with a specified minimum level of reliability at a minimum deployment cost is addressed. This problem is coined the minimum cost reliability constrained sensor node deployment problem (MCRC-SDP). The MCRC-SDP is proved to be an NP-Complete. An ant colony optimization algorithm coupled with a local search heuristic is proposed as a solution. Extensive experimental results demonstrate the effectiveness of the proposed approach in finding high-quality solutions to the problem.