How do you enable the Service Cloud Console in a developer org?

First go to your profile and activate "Service cloud User" option. Then try again with service cloud console app :)

Is this an old developer edition? The service cloud console hasn't been around for that long, so it may be that the template for your dev org didn't include it. I have a similar org that doesn't have knowledge feature license. If that is the case, you can either raise a case with support to have the feature enabled or just spin up a new dev org. I usually choose the latter as its faster.