Помогло в итоге в методе run() добавить
if (Looper.myLooper() == null){
Looper.prepare();
}
Полный листинг
private void refreshUserCoordinates(final Context contextThread) {
Intent intent = getIntent();
final String user = intent.getStringExtra("user");
Timer timer = new Timer();
timer.schedule(new TimerTask() {
@Override
public void run() {
if (Looper.myLooper() == null)
{
Looper.prepare();
}
GeoPosition geoPosition = new GeoPosition();
geoPosition.SetUpLocationListener(contextThread);
ServerInteraction serverInteraction = new ServerInteraction("http://razdvatri.ru/refreshCoordinates.php",
"{\"user\" " + ":\"" + user + "\", \"latitude\" " + ":\"" + geoPosition.getLatitude() + "\", \"longitude\" :" + "\"" + geoPosition.getLongitude() + "\"" + "}", "put");
serverInteraction.execute();
}
}, 0L, 50L * 1000);
}