A covert communications network is an overlay peer-to-peer network used to support communication within a group in which the survival of the group depends on both anonymity of communication and concealment of network membership to other members of the group and to external eavesdroppers. These requirements are much more stringent than for typical privacy and anonymity systems. Whereas anonymity systems often reply on a series of intermediate network participants to forward messages in a way that de-links the sender from the receiver, membership concealment relies on the topology of the network. In this paper, we consider the topologies of resilient covert communications networks that minimize the impact on the network in the event of a subverted node and maximize the connectivity of the survivor network with the removal of the subverted node and its closed neighborhood. We briefly describe necessary considerations for the generation of covert communications networks, and then develop general methods for constructing arbitrary-sized near-optimal network topologies.