Dog pooping on rental property?

I live in a street with several duplexes. The couple sharing the unit I'm in have a dog that they let out into the backyard to use the bathroom. Even though there is really nothing in the lease about use of the backyards, I'd assumed that each person was pretty much renting the piece of yard directly behind their unit. My neighbors let their dog out, and it is constantly pooping on my side of the yard, as well as other people's yards (but mostly mine). Of course, they do not clean up after it. Our city has an ordinance about dog sanitation, basically saying you must clean it up when it is not on your property (not to mention leash laws). Since I don't technically own the property, do I have any legal recourse? And yes, I know I should talk to the landlord, and I will, this is more hypothetical, or in case the LL does nothing.