I can't quite remember how I came across it, but I eventually discovered Sweet PDZ. It is a horse stall refresher, but is effective for other animals as well. It captures and neutralizes ammonia.
It is organic, safe, and inexpensive. A 25 lb bag costs me approximately $10 at Tractor Supply. Last summer I went through three bags.
It works incredibly well. When I first started using it last summer, there was an odor around a couple of trees in the back yard that the boys frequently peed on. I sprinkled it around the base of each tree, about 16" out, and also sprinkled some on the trunk itself. I used a heavy hand the first few times I applied it. Within an hour the smell was gone. Les was particularly amazed, which is impressive, because he is pretty skeptical.
It is a granular powder. I apply it with a cup. It is drying to my hands, but not harmful, I am sure.
The heat and lack of rain led me to use this about three times a week last summer, with great results. So far this year, I have only applied it twice, because we have been getting rain.
I highly recommend it to anyone with any sort of animal. It can also be used as an add-in for cat litter, and has various household uses.