Wow, i am having an identical problem. Even had a very long thread on the topic which got closed when our neighbor's mother stalked me on BYC to rant at me.
Here's the thing i have found, talking to cat owners rarely does any good. There are people who feel their cats have a right to be outside and do whatever they want, and they personally don't care what damage they cause. So others have to suffer with ruined gardens, injured or killed pets, and the horrible sounds of cat fights wafting through the night. All that being said, i love cats. i just keep mine safe and sound in my own house.
Anyhow, some suggestions i received were shooting the cat with a super soaker (for range and accuracy). Use vinegar water and perhaps a little food coloring so the neighbor knows the cat has been in your yard. Although with the food coloring you run the risk of the neighbor trying to accuse you of harming their cat. So maybe just the vinegar.
One option i'm exploring with my neighbors is to top our mutual fence with something, like wobbly hardware cloth or aviary netting that curves inward towards their yard so the cat can't get over the fence. This may only work in our situation as their cat tends to come over at a particular spot. Were the cat to come over farther down they would be where our goats roam and the goats are so curious they tend to scare cats out of that area.
Some people suggested to me to get a dog, but that comes with another whole host of problems. And who's to say the dog won't end up attacking your ducks? Animal Control suggested i get a mean rooster (my hens have voted a resounding "NO" on that option). They also suggested getting a peacock or geese. But again, that would entail me taking on another animal, more work, and i'm not up for that.
i'm not sure how air soft guns work. Are those the air guns that shoot little plastic balls? i've seen neighbor kids playing with them, shooting each other, but don't know how much that would sting a cat. So i'm thinking a super soaker water pistol might be your best bet.
Okay, last suggestion is to keep your ducks penned all the time. Totally not fair that you have to pen your pets because someone else feels their cat has a right to your yard, but that's unfortunately the way it is when you're dealing with unreasonable neighbors.
Good luck, and let me know what you try and what works for you.
