I'm sure you can find an organic type cleaner and use it, but it will not be specifically designed for cleaning carpets. I use Basic G and Basic H, their fumes are bird friendly and do good cleaning and deodorizing when you spot clean. I mix the two in a spray bottle with water, spray the spots/s that needs cleaning and then dry it all up with a towel.
However, I do remove the birds from the coop or area to be cleaned when I'm spraying the Basic G/H spray.
Treesa -- Thanks. Looked these products up, they look good. Thanks again for the recommendation.
I was in a store once a few years ago, looking at cleaning products, and asked one of the store folks whether the product was pet-friendly, and a woman standing a few feet away said "I love hearing people ask that question, looking out for their pets."