We propose a time slot based transmission strategy, referred to as adaptive coordinated napping (CoNap), for energy saving in cellular networks under time-varying traffic demand. In adaptive CoNap network, multiple neighboring base stations (BSs) form a cluster and each BS operates in either a transmit mode (TM) or a nap mode (NM) in each time slot. The dynamic assignment of TM and NM to each BS is implicitly coordinated among multiple BSs. This implicit coordination is realized by a binary general flickering pattern matrix (FPM) through adaptively selected mapping matrix (MM). To track the time-varying traffic demand, we develop an adaptive algorithm to dynamically select the appropriate MM from a predefined MM set by taking into account the network quality of service (QoS) requirement. Our numerical results based on a realistic energy consumption model in a cellular network show that as high as 40% saving can be achieved without compromising the network QoS.