Pinning down Carl is a matter of understanding his mobility problems. He has Nirvana to limit yours, so his mobility can be horrid without it being obvious at first glance; but it is. Use Dnails to lock him in one spot, but only after you've confirmed that Nirvana won't get in the way AND he has no way to dodge them. Not wasting nails is very critical.
Also, A nail dash is hugely helpful for regrounding yourself and to be tricky in your movement. Being unpredictable in movement and momentum is very useful, as Carl can't control nearly as much space as he wants you to believe. In any case where you can poison nail dash (Which is, air dash immediately cancelled by a poison nail; causes you to land much much faster and leads your fall with the nail) and in any way put Carl in blockstun, you should take it, because it completely deactivates Nirvana, causing, obviously, nirvana to not be able to hit you, and wasting his doll meter. Uses only one nail, extremely useful in this matchup.
Mostly though, just be extremely patient, the more you force Carl to try to control space, the more meter he doesn't have anymore.
If Carl is playing too patient, or even if he isn't, try to get a connected A and C bumper out. The mobility and mixup it grants you is extremely helpful, and he has extreme difficulty hitting you for putting them out if he's full screen.
When you're stuck in the sandwich, block. Block well. Hold low block, reaction block his overheads. If you get hit, he's almost surely going to reset you; same deal, reaction block low, but if you notice any of his significant reset notifiers (2D, 3D, 6C) try to react accordingly.
Good luck, ask any other questions you might have.