To exploit the full potential of radio measurements of cosmic-ray air showers at MHz frequencies, a detector timing synchronization within 1 ns is needed. Large distributed radio detector arrays such as the Auger Engineering Radio Array (AERA) rely on timing via the Global Positioning System (GPS) for the synchronization of individual detector station clocks. Unfortunately, GPS timing is expected to have an accuracy no better than about 5 ns. In practice, in particular in AERA, the GPS clocks exhibit drifts on the order of tens of ns. We developed a technique to correct for the GPS drifts, and an independent method is used for cross-checks that indeed we reach nanosecond-scale timing accuracy by this correction. First, we operate a "beacon transmitter" which emits defined sine waves detected by AERA antennas recorded within the physics data. The relative phasing of these sine waves can be used to correct for GPS clock drifts. In addition to this, we observe radio pulses emitted by commercial airplanes, the position of which we determine in real time from Automatic Dependent Surveillance Broadcasts intercepted with a software-defined radio. From the known source location and the measured arrival times of the pulses we determine relative timing offsets between radio detector stations. We demonstrate with a combined analysis that the two methods give a consistent timing calibration with an accuracy of 2 ns or better. Consequently, the beacon method alone can be used in the future to continuously determine and correct for GPS clock drifts in each individual event measured by AERA.

26 pages. Replaced with published version. Added journal reference and DOI