A little late to answer but .....
There is no DESIGNATED tent spot in any Premium site. However, tents are often set up in the dirt/area just off the pavement on any of the three sides. Of course, not all Premiums are convenient in that respect (trees, brush, fence, etc.). But people like you want to add a tent.
Call the Disney reservation number and ask to have a note/request added to your reservation (commonly done) that says something like "Guest also has tent" or something like that. That comment on your reservation will get passed to the Fort along with your arrival info a few days before arrival when preliminary site assignments are made. The CM making the assignments will attempt to accommodate your request (and they are pretty good about trying based on what they should have available the day of your arrival).
When you arrive, even with early on-line check-in and the ability to by-pass the lobby/front desk, if I were you I would still go in and check in face to face and ask if the site being given to you will handle a tent.
Last option if you get to your site and think it won't handle the tent, if there is an empty one or few nearby that will, call the front desk or go back in person and they will swap you over the phone if possible (again, it might be already "checked in" via the early on-line method and can't be swapped even if it is empty - happened to me).
Good luck.
Bama Ed
PS - you can include the size of your tent in the comment to if you wish. "10x12" for example. The more info you give the Fort, the better your chances of a good fit.