I have found that my refuse stockpiles fill up fast naturally, but if I define a dump zone and flag the corpses for dumping, they will get moved more quickly

@joshuaalbers Dump zone would be my first suggestion. It may also be worth checking "standing orders" (capital O is the command) and make sure "dwarves gather refuse" is turned on.

I'm not sure "corpse " stockpile is what you want. Depending on the kind of animal (domestic or wild) these corpses may not qualify for that and you may need a "refuse" stockpile instead.

And you may need to disable other jobs on the haulers, because they always choose bad priorities.