How about a no pet rule;)

Is the pet yours? Or someone else's? If it is yours, you should be able to completely control that situation. If it is someone else's pet, then you need to meet with them and discuss the situation.

How about no patio, pdodd?

Could be a sleep-walking neighbor?

If it's a cat, you can't control it. If it's a dog, provide walks. Build out of materials that can be hosed down.

judiwithani- I can't think of a scenario where a cat would choose to urinate on a porch?

This will require some maintenence, but better this than urine. http://www.wikihow.com/Make-Homemade-Cat-Repellent

Also, check out: http://www.cat-repellant.info/html/diy-cat-deterrents.htm

Put up a nanny am to see what is doing it.

There are sprays available at the pet store to deter cats from the area. Also heard that half full water bottles strewn about make cats avoid the area. Doesn't look so great though. Agree with ASVInteriors -- it is probably the surrounding area and not the patio (if it's concrete or stone).

You can get motion sensors to hook up to a hose/sprayer to deter animals from getting on your patio. Most animals that mark territory do it on uprights, so a flat surface should be fine.

If the pet is yours, watch and do something deterring (spray water, if they don't like it) while yelling angrily when you catch them in the act. Keep watching and say something approving when they pee in a place that's okay or leave the patio. You need to do the praise, otherwise, the animal might conclude that you don't want them to pee, which they can't exactly avoid, rather than you don't want them peeing on your patio.

Get a mechanical toy to roam around the patio saying, oh, Howdy goo goo over and over. That might keep the cats away, hey, Karemore?

Not a mechanical toy, Chook - a MARVELOUS

Lime under the house is supposed to deter cats here.

Would lemons work?

Dogs on the patio deters cats here, Chook.

Lemon blossoms smell a lot gardenias.