You can potty train your birds. I used to watch Casper closely and whenever he did the little poop dance, I'd repeat "poop! poop!" and now he's learned to do it on command (: So about 20 minutes into cuddling or just chilling out on my head/shoulder, I make him step up, put him over a tissue and tell him to "poop" and ta-da! But even before he learned that trick, he never pooped on me. He's such a clean freak!

As for the poop stains on furniture/clothes, towels are my best friend. I drape them over my furniture when he wants to run around and play. Just make sure their nails don't get stuck with every step they take hehe.