If you can catch the cat (pick it up, or use a live trap): you could try putting a note on the collar, asking the owner to telephone you or email you (give contact info.) Then you could explain that the cat is not welcome in your yard.
Or you could catch the cat and try taking it to the animal shelter. They will probably contact the owner, but the owner will have the trouble of getting their cat back, so they might be more inclined to keep it home in future.
Or you could try an electric fence, which works well against many kinds of animals.
You could sit outside with a squirt gun or a water hose and spray it each time it shows up, but that is probably not practical.
I think I've read of water sprinklers with motion sensors, so they spray when an animal moves nearby. One of those might deter the cat.
You mentioned that a live-trap might catch chickens: that depends on where you put the trap. Maybe you could hang it on the fence, or sit it on top of the chicken coop, or set it only at night while the chickens are sleeping. And if a chicken does get caught, you could just release the chicken and re-set the trap. (I don't know whether the chicken will avoid the trap in future, or go back for another piece of bait.)
If none of these ideas work, hopefully they will at least help you or someone else think of something that does work
