Hello Econman,
Went through this when I purchased mine approximately. 2 years ago. It resided in Alabama also and did no have a title as Alabama only titles from 1975 to current.
The current owner will need to reregister it if the previous owner is not available.
Step 1.
Obtain a bill of sale from the current owner and make sure to have it notarized.
Obtain the current registration or a notarized copy of it.
Step 2.
For a Tennessee title go to this web site:
http://tennesseedriverslicense.org/official-forms.html
and click on this form:
Car Title -> Certification Of Ownership
You will need to fill it out and explain that the State of Alabama does not title vehicles back prior to 1975.
I stated on mine: "The State of Alabama does not require a Title for vehicles of 1974 model years or older under Code of Ala. 1975 Section 32-8-31 parg. 12"
With all this in hand, I went to my local DMV and filed for a title and left with my registration and tag. The title came by mail several weeks later.
Please remember that your mileage may vary at you DMV as not all clerks know what the laws are.
Hope this helps,
Charles
CC's72