I've seen video tests of pee/poo verses the house-cat. Felines are curious - the waste of other unknown animals only draws them to investigate the poo/pee. Even big cat scat.
Pepper based products only work until the first time it rains or it gets wet out.
Ultrasonics are a waste of money.
Water scarecrows can lead to all sorts of problems for your plants, especially if your yard is "busy".
IMO, you have a couple of PRACTICAL choices.
1. Trap the cat and take it to the humane society. The humane society often has traps you can borrow.
2. Scatter marble sized (or larger) gravel as mulch in the areas the cat is bothering - if a cat can't "scratch", it generally won't do its' business.
3. Place thorny stems from rose bushes or barberry around the area the cat is bothering - no one wants to step on thorns.
As far as I know, these 3 things work more often than any of the other suggestions and don't cost anything to try, unless you have to buy the trap or gravel.