I picked up Portal 2 and wanted to try co-op with my son. We have two computers, but just one Steam account. Usually this is fine since I just leave the family computer in offline mode. Unfortunately it would appear that Portal 2 only does co-op when Steam is online.
As it sounds like you're aware, you cannot be logged in to Steam in two separate locations at the same time (unless one or both are in offline mode, and thus unable to play online).
Edit: Suprisingly, it looks like you can play with Steam offline over a LAN:
Go to "C:\Program Files (x86)\Steam\steamapps\common\portal 2\portal2\scripts" or to the relevant folder or drive where you installed Portal 2. Now you have to add the following code in "extras.txt":
Select Start LAN on the host computer and select Connect on the computer. Then the host should select Start. Make sure the IP Address is correct for the HOST.
Alternatively you can use the console: