If you use the Git installer for OS X, it'll do a system-wide install. This means you need admin rights for it to run.
However, the installer will write everything to /usr/local/git. This path (/usr/local) is not used in a default OS X installation. Per the Filesystem Hierarchy Standard, you can place anything there which just belongs to one user, and safely remove it again without affecting anything else.
If you ever want to uninstall Git – at least the version from the Git Installer – run the following:
rm -rf /usr/local/git
rm /etc/paths.d/git
rm /etc/manpaths.d/git
The first folder is the one containing all the programs. paths.d/git is just a file that enables the git for every shell's path, and manpaths.d/git does the same for the manpage.
Removing the above files and folders will have no implications whatsoever for the other user accounts.
The GitHub for Mac application can simply be installed to /User/your-username/Applications instead of /Applications. You might have to create the folder if it doesn't exist yet.
Other users won't be aware of this application at all. Its settings will be stored in ~/Library, which also belongs to your user.