I haven't personally ran a CS:S server, however I have built a CentOS 6 based Cod4 server. The primary thing you need to determine is how are users going to connect to this second server? Are you going to bring up a second static IP, or are you going to utilize the same IP? If you are using the same server IP as your existing server, then you need to configure your new server to use a different port. ( Example for cod4: IP:28960; IP:28961; IP:28962; etc. for each server )
Ensure your iptables rules ( firewall ) allow traffic to flow on your newly assigned ports. Start your second daemonized server process with the new configuration, and you should be golden.
If your having issues starting a second server process, that's where I can't help you. In the call of duty world, each server has a "game folder" that contains the mods, configs, game files, etc. You just duplicate it, execute the same dedicated server program with the newly modified command line and your set.