I stand by my counter picks:
Battlefield 50:50 at best.
Lylat Cruise 45:55
Rainbow Cruise 55:45
Frigate Orpheon 50:50
The others seem fine, but... Rainbow Cruise? No.
Rainbow Cruise
40:60 ZSS's Favor.
It doesn't seem logical since there are few recovery ledges for Zero Suit's tether recover to work, but you have to take into consideration how well ZSS can take control in the air. Players can't stay still and bait out attacks from her on this stage, they have to keep moving and she can easily punish them as they're doing so. That eliminates ZSS's largest problem.
Baiting.
Zero Suit Samus has extremely high jumps to make up for her lack of a decent recovery on this stage, and the most horrible part of it all, is the fact that her tether recovery WON'T have anything interfering that it will sweet spot on. That means she can use her plasma wire as a mobile offensive measure. Yeah, you might not need to worry about it too much until your percent is high, because a good Zero Suit wouldn't want to get you down below her, especially not Captain Falcon. If you're above her, that's exactly where she wants you. One thing to watch out for, is when you're on a platform, she can reach the plasma wire through them. Even if they're solid structures.
The most deadly part of this stage is the pendulum platform. While it's swaying back and forth, she can simply use her up tilt (silly as that sound, it has a lot of range) and it will smack you up into the solid platforms above, causing a stage spike. This applies for just about any character, even Falcon can do it with his up throw. The only problem is ZSS has a really, really easy time with forcing her opponents around where she wants them. Getting close to her without getting Down tilted / Up tilted / Up smashed is far more of a struggle than you may think.
Another note: Characters move with the stage if they're down smashed. They don't stay in one place. However, when the stage begins restarting it's cycle and both players are forced to go down to to lower level of the stage and back on the ship; ZSS can use a down smash to keep you up above the platforms. If that doesn't kill you, it still gives her enough time to get down below you and punish as you're scurrying down to the ship.
I usually take people to Rainbow Cruise with Falcon too, since it's such a good stage for him. But against a Zero Suit? I would much rather take her somewhere else. Falcon can't really fend off characters that he can't approach - - and that have a much better air game than his own.