Actually, you can do it easily with LOGIN table.
Look at page 143 of Stat Server User Guide: you have a Login table and there are several fields in it. The ones you would like to focus on are:
Status, Time,AgentDBID
When agent logs in, Stat Server writes the time when the agent logged in into Time field, writes '1' into Status and then writes Agent's CME ID in AgentDBID.
When Agent logs out, Stat Server writes the time into Time field, '0' into Status field and Agent's CME ID into AgentDBID field.
There are several things you should be clear about:
1. Time is in UTC format. In other words, it is written as a number of seconds since 1970/1/1 12:00 . Don't ask me why they did it, but this is how it is, so you will need a function to convert from it into normal human time. (Ask me or anyone else if you need it)
2. AgentDBID IS NOT Agent ID. It is a reference cfg_agentid or cfg_person table. Just find the same number in that table and then you will find your agent id.
What are you using to see the results? Excel? Access? ...Brio?
Actually Brio would be really simple. I am an engineer so I am not going to get into the licensing issues: I assume you have the license.

Drop me a line if you want me to give you a sample Brio for agent login/logout reports.
Vic