I've found that setting a hunter on border patrol (the stop-sign icon) fulfills this function - although canines are, in fact, a little better at this. For the hunter unit to come up to the same effectiveness usually requires the Hunter's Sight promotion, or some other way to improve the unit's ability to spot hidden animals.
For the most part, I'll normally put one hunter unit on patrol for every two to three cities I've got - that keeps the animals under control fairly well, and gives me a reasonably steady stream of subdued animals as well. I don't know if it's the way the AIs are programmed or if it's just a coincidence, but I have noticed that the hunters tend to focus more on encroaching animals, while the canines tend to focus more on barbarians and neanderthal units. That might just be the way the combat bonuses are structured, though - hunters are more likely to run into dangerous odds against barbs/'thals, while canines don't get bonuses against animals (unless suitably promoted).
The advantage to using the border patrol order is that the patrolling units are willing to go a bit beyond your borders to get a target. It gives your defenses a little more depth and proactive-ness, and can keep the animals/barbs/neanderthals from scoring easy kills on your noncombat units.