I highly recommend NOT Mark Twaining it when writing a Southern accent, which means writing out the accent phonetically. It will get very tiring for you to write, and also tiring for lots of people to read.
You probably can't represent the accent in speech very well, but the (general) Southern dialect's got lots of neat features that General American English does not use much. One is the use of doubling certain words: "over yonder," "up on that there table," "I might could go to the store," etc. Frequent use of these alone will work.
There are a lot of "grammatical errors" that are very common in Southern dialect as well, such as "don't" and "ain't" being used in specific ways like "I don't got no clue" or "I ain't playing around here." The word "was" is also usually used in the places where "were" and other be verbs were supposed to be, like "Them there orcs was a looking at me, son. We might ought to scoot on outta here."
Then there are certain words that are very common: "Fixing to" (about to); "fix a [glass of water]," "hankering," "reckon," and of course "y'all."
There's so many cool features of the (general) dialect that you can use.