I assume that the way the said animal is marking it's territory, and with reference to "They don't come at night when I sleep inside.", can I assume that you are camping there more than a night or two? If thats the case then I am hoping that its not a backcountry area where you have bears.
Marking the territory in the sense you are talking of definitely suggest that you're referring to domestic and more or less harmless animals, cats and dogs being the ideal examples. Assuming the way of marking the territory, we are not talking of big wild animals like Bears and Coyotes, etc.
So, as far as the cats and dogs are concerned, No matter what, Your best bet to keep tent as your territory should be zipping it neat when you go out and its unattended.
Yet, if you are looking for some thing that can keep them away, probably odors are best bet to bank upon: Apart from peeing around own tent, there are a few tricks to work it around.
- You can use a room freshener with a strong fragrance, that shall help you keep the dogs and cats away. Most of them are irritated by strong odors.
- If the room freshener for some reason is unacceptable to you, then you can try for something like putting mothballs into a Net-pouch, that can keep many insects and dogs away. That works for my dog, (Though we never intentionally try to keep her away from us, or out of our territory, she is always with us!)
- I've observed that such animals tend to occupy the corners. So if I were you, I would try and keep some stuff at the corners, but this really doesn't work on almost every situation though, at least never keep your bedding at the corners, they would really get tempted to take a nap there and often try coming in and snuggle. Instead, if its a cat (and not a dog for sure) you can keep your shoes or some other footwear (spare one of course if you carry along) at the corners, most of the cats tend to hate them, while dogs would love them. Keep the stuff at the corner, whatever stuff that won't make an animal feel cozy and comfy.
My pet, she loves sleeping on (and fortunately not inside) my sleeping bag and she does that all the time.