The momma will continue eating the puppy poop until the pups are 4 to 6 weeks old. Usually once you start feeding the pups (around 4 weeks) the diapering will slow down and you might get an opportunity to start picking up puppy poop if you are fast enough.
As soon as the pups are walking I put down a small double sided bowl of ground up dry puppy food. Just leave this dry food down along with a separate bowl of water and before you know it the pups will be eating on their own and mom will start weaning them. I always let the momma continue to nurse the pups so the weaning process is slow and not stressful to the puppies or momma.