Someone just mentioned calling a goat farm. I never thought of that but he said they come pick them up to feed the animals and much what they don't eat. I have to say, I never thought of that!
Send out flyers (or however else you communicate with tenants) telling them where to put them starting now. Post something by the dumpster where you really want them to place them; there will still be people who just toss them in front of the dumpsters though.