You could make a note against their record that they are logged in. Better, the time that the login was last used (this you keep updating as they use the site): If they log out, set the time to something way in the past.
When they try and log in; if the time is too recent (this depends on your users' usage), say that they're already logged in. If it's sufficiently long ago assume that they left the site and now they're logging in for the first time again.
Of course, it would be better to find out how multiple logins enable them to get around your security and fix that, rather than go for a bandaid "don't let them log in multiple times". Like devinemke said: "not very reliable".