The only way I've succeeded so far is to employ SSH.

Navigate to ~/.ssh and open up the config file. By default, it should look something like this:

Host *
  AddKeysToAgent yes
  UseKeyChain yes
  IdentityFile ~/.ssh/id_rsa
  ForwardAgent yes

1. In order for your Mac to be identified by two different GitHub accounts, you'll need to create SSH key pairs for each account.

• run ssh-keygen -t rsa -b 4096 -C "your_email@example.com"

• This will prompt "Enter a file in which to save the key". The default suggested filename would be id_rsa. Remember to name the new file differently if you have any existing one, eg. user-1. This will generate a private and public key, user-1 and user-1.pub, respectively.

2. Register the contents of the public key, e.g user-1.pub, into the respective GitHub accounts. Follow the steps here to do so

3. Head back over to the SSH config file at ~/.ssh and amend accordingly to:

#user1 account
Host github.com-user1
   HostName github.com
   User git
   IdentityFile ~/.ssh/github-user1
   IdentitiesOnly yes

#user2 account
Host github.com-user2
   HostName github.com
   User git
   IdentityFile ~/.ssh/github-user2
   IdentitiesOnly yes

Replace user1 or user2 with your GitHub usernames

4. Go ahead to git clone the respective GitHub account

git clone git@github.com-user1:user1/your-repo-name.git your-repo-name_user1

5. Configure your git identity:

• open up local git config git config --local -eand add:

[user]
   name = user1
   email = user1@gmail.com

6. Ensure your remote url is in the format of git@github.com-user1:user1/your-repo-name.git your-repo-name_user1

Now you can git push and pull all you like!

• Automatically use correct SSH key for remote Git repo
• StackOverFlow