When normal routines are perturbed by landscape-level events, wildlife may move toward new sources of water, hunting or forage. A coyote will eat a rabbit or a house cat with equal relish. Bears don't distinguish between wild berries and your berries. Mountain lions may develop a taste for goat or chicken if the deer population has been reduced through fire or floods.
In a suburban area, firearm deterrent of these major predators is likely illegal. Code where I live is no firearm discharge within a quarter mile of an inhabited structure, and then only into a backstop. So what can you do to protect your pets or small livestock?
Many good blogs and web publications address building varmint-proof enclosures for your chickens, rabbits, goats, etc. My favorite is Backwoods Home. Use their search for anything from regular to solar-powered coops. Probably some great plans for rabbit hutches, too. This post is not about that.
You can throw rocks to persuade varmints to leave your area. For me, that works if the critters are within 20 feet of me -- the old upper body strength in women thingy. If I have to get that close, I'm not going out to shoo! them away.
A slingshot can be as simple as a Y-shaped stick and some big rubber bands to a more expensive high-tech model like this or this fancy one. Ammo can be anything from pea gravel to steel shot. You can use big rocks or small. In most environments, running out of some form of ammo wouldn't be a challenge for a slingshot, even if you have to break into your pinto bean or mismatched nuts-and-bolts stash.
My choice is the old standard wrist rocket. You can buy one for $5 or more from eBay, yard sale or retailer or make one. What these all have in common are the very stretchy tubing and a wrist-stabilization system. My targets are usually raccoons, who love both apples and chili peppers in my yard and can get through my obstacle course of deer-defenses. The deer can be moved by just walking out and clapping my hands. They are also less likely to charge and bite me. I actually try not to hit them, just plink near them to get them moving.
You will need to practice. A garden glove may be helpful early in the process. Once you are a relatively good shot and start to use the weapon to dissuade wildlife, remember to aim for the hindquarters. You are trying to move them out of the area, not maim them.
If you goal is the kill the animal(s), you must check with your local law enforcement to find out who can and how this can be done. Don't be surprised if it's either expensive or prohibited. Also, killing one coyote is unlikely to dissuade the other 30 in the area from coming into your area.