@James Yoo - This is such a tough dilemma, these people have rights and deserve respect but so do you and your residents. It's especially bad for houses bordering the alley. My suggestion would be to pay a few college kids to canvas the neighborhood with a petition for the city council.
I have this issue in my neighborhood as well, Iacienga and Beverly. We have a Saban center and the Cedars ER a few blocks away on either side. Finally a petition was passed around the neighborhood and delivered to the council rep. A meeting was had and Sanitation did a major street/Alley cleaning and the cops have have started driving the Alley's more.
Don't pay them and don't do anything to antagonize them. the sprinkler suggestion would just have the homeless people confronting your tenants.
Who's on the other side of the alley? Maybe split the cost of putting in a large, non discreet security camera? This will help you make the case again the deification and urination which is illegal and could help you get the police etc to move them.
Also, use twitter - the LAPD does monitor twitter, so posting a few videos of illegal behavior could help get you action.