There are numerous tours like this one - http://www.sweetmagnoliatours.com/P_Deep_South_Group_Tour.php but I don't know of any that go by train.
Have a look at Collette tours (US company), they do several tours of the South focusing on several music cities, also Titan Tours (UK company) do some. They have one called 'Southern sights and sounds' that might be just what you want.

Amtrak trains serve Atlanta, Memphis and New Orleans. They don't go to Nashville, though it's easy to travel there by Amtrak Thruway bus from Atlanta. Bradt's USA by Rail guidebook by John Pitt has more information about these and all other Amtrak routes.

It's probably worth pointing out that Amtrak's routes between major cities away from the East Coast are less frequent than you would probably expect and it is quite reasonable to arrive in a city at some unGodly hour of the morning which automatically causes an onward journey and safety issue.
On our major trip (7 weeks in the USA as part of a longer trip) we initially booked a 30 day Amtrak train pass but after planning using schedules and length of journeys we opted for internal flights instead which were reasonable on carriers like Southwest.

Personally, as the area you are hoping to cover is not the greatest I would hire a car and do it yourself. You will of course have some long drives included on certain days, but getting from Memphis to Nashville for example is an easy 2.5-3 hours along the Music Highway.

will need car for 2 weeks is it as expensive as florida to hire one

I believe it is much cheaper to arrange car hire in the UK before you leave through companies like http://www.carhire3000.com and http://www.netflights.co.uk

luci

On the trip I mentioned which is a few years back now we used http://www.dollar.co.uk everytime we needed a car during the 7 weeks in the USA. If you book with them it is cancellable so if you find a better deal then you can go for that.