Find a suspicious dirt pile. (Long Update by 2 days, long update works for spawning new animal tracks).
Track it until the animal spawns at the end of the track.
Keep the animal alive at the end of the track (for zoos, pens, goat farm, whatever reason) AND don't shut down the server.
A new animal will not spawn unless the animal at the end of the track is killed or the server is shutdown (which is not always possible).
VOD of my bug testing to verify that this is what's happening. The link auto starts at the selected timestamp and the testing ends at 1:53:09:
Previous report here for more information:
Follow the instructions above. Refer to VOD for in-depth testing.