Bo and Bea both potty on rocks or grass -- and they have both available in their dog yard (or "meadow" as I am currently calling it). I would LOVE it if they both only peed on the rocks. (or in your case, the cement) Bea's pee turns the grass yellow while Bo's does not. The other side affect to the rock-peeing is this: Bo pees the SECOND he gets off the steps and that means MUCH built up pee pee under the rocks. Add that it never dries out there (shady, moist side of the garden already) and you've got yourself a stinky stinky situation! You step out onto the porch and, in the heat, it's nose burning. Seriously. Nose burning. Solution? I went out and got a few boxes of baking soda and liberally applied one of them to the rocks area (river rock path) and "stomped in" the baking soda so it would fall betwixt the rocks. Baking soda is a naturally occurring substance so it doesn't mess with my organic fung shey around here. WORKED GREAT!!!!!
Perhaps you could make a gravel area for peeing in your new yard? I'm telling ya, you won't regret it! Makes pick up and clean up a BREEZE!
Oh I have some great suggestions and will be back later. I went through this with Jack (our pitty rescue at 4 months) and now Sally. I have success with Jack and Sally is getting there but she did pee on the concrete steps this morning. They will get it though!! I'll be back.
Three Hooligans and 1 Angel - Wilson, Sally, Emma & Jack