Does TN issue non resident permits, and if they do, how do I obtain one
Officially, Tennessee does not issue non-resident permits. However, as I understand it, if you work in Tennessee for six consecutive months, you can obtain a Tennessee permit (essentially, if you work here for six consecutive months, you are treated as a resident for purposes of the permit).
I should note that, if you're just coming here for occasional visits, don't worry about getting Tennessee's permit. Tennessee recognizes all out-of-state permits, even non-resident ones (like New Hampshire, if you're age 18-20).
EDIT: Just make sure you have a permit from some state! No form of carry (concealed, open, or car) is allowed without one.