This is one of my favorite topics, you should read some of the past threads, several circuits that you might draw some ideas from. Let state, that I don't cats, or any animal for that matter, just as longs they don't use my property for their personal toilet.
Ultrasonic doesn't work too well, it's just a loud noise to animals. Once they figure out there is no physical threat associated with it, they ignore it. Some cats prefer a quiet relaxing place to leave their business, so they take it elswhere if they can, matter of convience. I've got mine set up to give a short blast every 30 seconds, through 4 speakers across the front of my house. Cut the traffic down considerably, but still have two cats occasionally. It might not be entirely the noise though, the neighbor is down to 6 adult cats and 4 kittens, from 17 adults previous. His property was seriously over populated, and I got the overflow.
I was getting ready to build an R/C Airsoft solution, but doesn't seem necessary right now, and so many other things to build.
Had a PIR idea I never got too far on... Sound alone wasn't as effective as I had hoped, start using firecrackers, which sent them up the fence just by opening the door. So figured I'd put the flash from a disposiable camera, a PIR, and ultrasound together in a solar charged landscape light. Unfortunately, the flash fries pretty easy over about 2 volts, and draw a lot of current, or atleast a lot of waste in down converting from 9 volts (PIR unit needed). Moved on to other projects without solving that problem.