you could try controlling the animal population by not letting it get so out of control
Keep the pets at a minimum, cage up any excess ones to keep them from reproducing. Immediately cage any newborns (especially kittens). Then they can't be adopted, so no more pets, and no overload.
I usually don't even keep pets. I don't really find vermin to be a problem, and I can take care of invaders with military and traps without the need for dogs. Every horse I get at the start gets immediately caged or butchered. If I get immigrants with a bunch of pets, I'll arrange for them to be incinerated (send owner into magma chamber, let pet follow, send owner out, lock door, etc.) The dwarves get over it - at least I'm not burning THEM up.
-edit- ah, I just read one of your posts more carefully and realised you said the need for BONES. If you really need the bones (and only the bones), you could turn off automatic butchering, make a flood room near a refuse pile, add in a few chains, and just assign extra animals there, flood the room, and let the bodies decay to bones. Although it may be easier just to chasm the extra fat every so often.
I never really need extra bones myself, I always get piles and piles of them from frequent chasm attacks (mostly ratmen) and especially sieges - that last goblin siege left me with 150 extra bars of iron and more bones than I could count. I also got a bunch of caged goblins which I stripped down (chasming/melting items off them) and used for target practice for my marksdwarves.
[ March 23, 2007: Message edited by: Paul ]