(I've voted to close this as a possible duplicate, but I might as well add a similar answer anyway.)
When using the SSH transport, GitHub identifies you as a user based on the SSH key that you use to authenticate.  So, you need to make sure that git is using one SSH key for one repository and another for the other.
I'm going to assume that:
- You have a GitHub account called user1, and you've added to that account the public key corresponding to your local private key/home/whoever/.ssh/id_rsa.  Let's say that the repository you're interested in accessing asuser1isuser1/whateveron GitHub.
- You have a second GitHub account called user2and you've added to that account the public key corresponding to your local private key/home/whoever/.ssh/new/id_rsa.  Let's say that the repository you're interested in accessing asuser2isuser2/whateveron GitHub.
The simplest way to do deal with this is to create a new "remote" (i.e. a nickname for a remote repository) for each repository, where the hostname is in each remote's URL is actually an alias that you've set up in ~/.ssh/config.  (If that config file doesn't exist, you'll have to create it.)
For example, one entry in the ~/.ssh/config file might look like:
Host github-as-user1
  HostName github.com
  User git
  IdentityFile /home/whoever/.ssh/id_rsa
Then you can add a remote called gh-user1, say, with:
git remote add gh-user1 git@github-as-user1:user1/whatever.git
... and then if you want to push your master branch to the repository user1/whatever on GitHub using the ~/.ssh/id_rsa key, you can just do:
git push gh-user1 master
In order to push as the other user (user2) to the second repository, you need to add a second alias to you ~/.ssh/config file.  For example:
Host gh-as-user2
  HostName github.com
  User git
  IdentityFile /home/whoever/.ssh/new/id_rsa
Then to push to that second repository as the different user, you can just do:
git push gh-user2 master