Source location privacy is an important issue in sensor network monitoring applications. It is difficult to be addressed by traditional security mechanisms, because an external attacker may perform simple traffic analysis to trace back to the event source. Solutions such as flooding or using dummy messages have the drawback of introducing a large amount of message overhead. In this paper, we avoid using network-wide dummy messages by utilizing beacons at the MAC layer. Beacons are sent out regularly, which essentially forms a constant-rate of dummy messages. Using beacons to replace the dummy messages may increase the delivery delay of event information because beacons are only sent out at the predefined beacon interval, but this latency can be controlled. To do this, we propose a crosslayer solution in which the event information is first propagated several hops through a MAC-layer beacon. Then, it is propagated at the routing layer to the destination to avoid further beacon delays. Simulation results show that our cross-layer solutions can maintain low message overhead and high privacy, while controlling delay.