I don't think it's currently possible to do so via the GUI, but the following should work, albeit be a little kludgy. YMMV.
Add the following line to /etc/sudoers (use
sudo visudo to edit the file):
%packageinstallers ALL = NOPASSWD: /usr/bin/software-center /usr/bin/apt-get
Then you just need to create and add the specific users to the
$ sudo addgroup packageinstallers
$ sudo adduser jdoe packageinstallers
jdoe can do the following:
$ sudo apt-get install <some-package>
and you can edit the desktop menu item for the Software Center so that it call on
software-center prepending the command with
PolicyKit may allow you to do so without sudo, but it's beyond my understanding at this point.