If there is another good tenant applying for the property, why not just rent to them instead? I suppose this depends on how difficult it is to fill a rental in your area. My hunch is that if they are already trying to customize a property that isn't theirs, perhaps they are unclear on the concept.
A few years back I had a tenant that asked if they could put in a garden. Got a neighbor to come over with his tractor to prep the beds, brought in good soil, etc. They paid for all of it. It wasn't anything fancy, but by a renter's standards, they felt it was a big deal. I'd say they put a couple hundred dollars into it.
Surprise! Two or three months down the road we are having problems with them paying rent among other things, so we give them 30-day notice to terminate their monthly agreement. An argument ensued, with them demanding to either be reimbursed or get help moving the garden. I'll leave the rest of the exchanges to your imagination.
I also like Matt Devincenzo's suggestion, if you have to go with the fence. I'm also saying this as a former renter many years ago who poured love and money into little beach bungalows, replacing flooring, adding fencing, gardens, paint, you name it. But if you are viewing your properties as a true investment, then that's what they are.
It can be hard to straddle the line sometimes, but I've been burned by other tenants as well (painting, extra roomies with paid utilities, spraying cats) so in my opinion if its a fairly easy place to rent, why stress over someone who is already causing you angst?