This paper studies the synchronization problem for a network of identical discrete-time agents with unknown, nonuniform constant input delays. The agents are at most critically stable and non-introspective (i.e. the agents have no access to their own states or outputs). There exists full state coupling among the agents. An upper bound for the delay tolerance is obtained which explicitly depends on agent dynamics. For any unknown delay satisfying this upper bound, a controller design methodology is proposed without relying on exact knowledge of the network topology so that synchronization in a set of unknown networks can be achieved.