What about rats, mice, bats, squirrels and raccoons?
Not a direct answer to the OP but I think a motion activated sprinkler would solve this problem –
http://www.absolutebirdcontrol.com/products/scarecrow?gclid=CPWq_MSA9acCFULf4Aod0XY4bw
Where did you say you live? 
Exploding fish decoy!
In the county I live, you can legally kill an animal on your property if it is harming one of your animals. However in the city I live it is illegal to discharge a firearm or bow and arrow. I think this is pretty common around the mid west. So if I were in your shoes I would be forced to become creative.
I worked with a guy who lived next to a house that fostered a large ferril cat population. The cats ran the neighborhood and liked to stalk his multiple birdbaths he kept in his garden. He said he had good luck with trapping them and dropping them off at the shelter. Honestly I think he started skipping that last part. I say if they have identification, drop them off at the shelter. The 2nd time the owner has to pay 80-100 bucks to bail mittens out of jail; maybe they’ll keep the stupid thing in the house.
In Wyoming, it’s generally encouraged to shoot stray cats. That opinion was common in Northern Michigan when I lived in that state as well. They prey upon native game birds, songbirds, and other desirable wildlife.
http://www.pictures-of-cats.org/fremont-county-wyoming-sheriff-shoots-any-cat.html
You can also shoot lions legally in Wyoming, both with a hunting license and for livestock predation:
http://abclocal.go.com/ktrk/story?section=news/bizarre&id=7194695
Are cats and raccoons really good at catching fish? What do they do, wait until one swims by, and then swat it out of the water?
Not many rats and bats around here…but many squirrels and raccoons. A few years ago I looked into what the laws were dealing with them. It was illegal to kill them by any method and had stern punishments if caught.
Pretty much.
My local town ordinance on pets makes it illegal for the cat to even be on my property without a leash. I can call animal control to remove it, or, if it is a repeat offender, the owner will be fined.
Those who own animals, or allow attractive nuisances to cause animals to congregate in an area are generally responsible for the consequences of the behavior of those animals. The Cat Lady who just can’t stop putting out cat food in her back yard, is legally responsible for each and all of the 875 cats that congregate there. (an actual case here in my area.)
Tris
Wow, that’s quite a difference from what most people are saying about their own jurisdiction. If it’s not too nosy a question, do you mind sharing at least what town/county you’re in that has laws like that? It it is too nosy, my apologies…
I’m really surprised that no one has suggested restocking the pond with piranha yet. That’ll have you covered for cats, coons, dogs, snakes, just about everything.
Including obnoxious neighborhood children.
You aren’t allowed to kill rats?