When we first got Zeus, he was AWFUL about peeing on the carpet. What I did was, at night, turn off all the lights and take a black light to everything. WalMart sells them in these long tubes/holders for like...$11 or something like that. WORTH IT!
Then I just sprayed the area until it no longer illuminated under the light (it's bright green).
Here's the light:
Lights of America Blacklight, 24 Inch Blacklight, Fluorescent Blacklight Bulb, Blacklight Fixture It comes with an on/off switch in the container/fixture.
We were using the white bottle of Nature's Miracle, but the red bottle worked better, IMO.
We have cream-colored carpet, also a rental.