The first thing you need to remember is your new puppy is a BABY! You would not spank your child for dirtying their diaper. And at 2 months old you also would not expect your child to climb up on the toilet. It takes time with your child it will take time with your puppy. I suggest no discipline for accidents. And, they will happen.
So now you're thinking if I can't correct him how will my puppy learn. I did not say don't correct your puppy I said don't discipline there is a difference. Dogs respond to positive reinforcement better than fear. Think about it, do you want your dog afraid of you? Of course not you want a loving loyal companion that is happy to see you and comes when you call.
Don't give your puppy run of the house. The area is too big and puppy will soil and come back to you. You won't know until you nearly stepped in it or got a wet sock. Then you may be angry. I suggest a pet safe area perhaps with vinyl flooring that makes clean up easier. I am not suggesting to leave your puppy penned up in your kitchen. Certainly take your puppy with you, but there will be times when you need to complete a task and your puppy is still insight. Crate if you have to because what you need to do is out of sight from the pet safe area. If you do crate and are ready to take your puppy out, have leash and treats ready straight out the door. I think it's very important to be involved as much as possible in the process. Don't just shove your puppy out the door. Lead your puppy to the area YOU choose for potty. Encourage by saying go potty or just potty. If puppy goes make a big deal! Treats, hugs, lots of petting ect. Reverse that and puppy didn't go outside but as soon as you are back inside he swoops and poops. Say no or no no clean it up quickly don't make a fuss. You will get frustrated keep cool and calm about accidents. It's a task but you can do it.
To review
Be involved, you are going to walk your dog anyway so go out with your puppy on a leash.
Lots of praise and treats for successes. Quick clean up and a simple no for accidents.
Don't let puppy have run of the house restrict him to a area that is easily cleaned up and where you can see when doing your daily tasks.
I make it sound simple and to be honest sometimes it is. I have had dogs trained at 10 weeks. Our sire Bentley was one. Only one time has he ever pooped in the house. And that was my fault. I took puppy out very early and he wanted out. I thought he just wanted to play so I told him no. Well he left me a present. I saw it when I got up I swear he was embarrassed went and hid in his crate!
Here is a little guide that may be helpful. Remember at 8 weeks puppies are pretty much in one end and out the other. So be ready for out shortly after feeding time.
At 2 months no more than 3 hours can your puppy likely hold it.
At 3 months no more than 4 hours
At 4 months no more than 5 hours
I think you see where that is going.
That is just a rough guide all dogs are different. Watch your puppy learn his signals. Before you know it you pup will be house broken. You'll be happy and your pup will be happy getting praise and loving. You will have bonded with your pup too!
Oh one thing I forgot! Your pup will want to go in the bathroom with you. I assume he wants to make sure you're not going on the floor? I could be wrong but....German Shepherds are just that smart!!!
Love Your DOG!!!