Might want to look into https://pyd.io/ which has its own APIs you might be able to figure into a CMS.
Are you sure a CMS is what you are looking for? There are systems like https://www.activecollab.com/ and http://collabtive.o-dyn.de/ that do a whole lot, and sometimes hacking together something for a CMS isn't the best solution.
There are some free/cheap solutions to time tracking that you can download and use on your server. http://collabtive.o-dyn.de/ is one. Though there are collaborative support softwares that work great as well.