I can't seem to find the answer online. Is it "She had a southern accent" or "She had a Southern accent"? (I'm from the U.S. and talking about someone from the southern states.) Thank you!
Notice that you have written 'southern states'. However, I am sure that there is no single right answer. In a text about the various regional accents in the US, it would probably be capitalized.

A southern accent, in general, is an accent characteristic of the southern part of any country or region. With reference to the English language, the term usually refers to either of: Southern American English (spoken in the Southern United States) English in southern England (spoken in South England) (Not a particularly reliable source, though: Wikipedia)

Some more reliable models, perhaps:

Thinking with a Southern accent. These are musings and random thoughts of a Southern newspaper journalist available for anyone with too much time to kill.

The distinct drawls and twangs that dominate America's Southeast as we know it may be dying off, new research suggests. A North Carolina State University study has noted a gradual shift away from the drawn-out vowel pronunciations widely associated with Southern speech, which experts say is 'disappearing'.

Stephen Colbert, on the other hand, born in South Carolina, felt that a Southern accentwould hold him back professionally.
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The name of a region gets capitalized. When in doubt, use lowercase. An American from the American South has a Southern accent. The West. The Northeast. The northeastern states. The west of the country. Georgia is to the south of Tennessee, but both states are in the South.

When referring to a group of people from a section of the country, or to what that group of people does, the reference is capitalized. Thus, She had a Southern accent or Southern drawl is correct.