Ask her why she likes the name Tennessee. Maybe she's always wanted to go there; maybe she thinks it's a nice place? Maybe she just likes the sound of Tennessee!
Tells her that there are plenty of other place names that can be used, because people use them all the time and it's no big deal. A huge number of names are place names, and people don't connect them to places at all. An example would be Charlotte. Charlotte is a city in North Carolina but it's a beautiful girl's name as well. People don't get teased for having a name like Charlotte (generally). If she really wants to name her daughter after a place, city, country, state, or something similar, suggest other ones. If she doesn't like your suggestions, tell her to search for other ones.
I wouldn't worry too much about January. Yes, it's not exactly the most popular girl's name but it's still only her middle name and therefore most people won't know it.
Explain to her that kids get bullied all the time in school, especially when they're young. Would she want her daughter to get teased at school because of her actions by naming her something that isn't exactly a name? What about when they're studying history in school, or about the USA? Tennessee will come up, and Tennessee isn't exactly like naming your kid London or Paris; they're a bit more usual, and more popular when it comes to place names than Tennessee.
If she doesn't think that her child will be teased (or refuses to believe it) ask her if she's thinking about her daughter's future. Most likely, she's just imaging a little baby girl, at the most 2 or 3 years old, named Tennessee January. She might think it's cute. What about when baby Tennessee grows up, manages to get through school without any incidents, and then decides that she wants to be a doctor, or a lawyer, or police officer or a principal or a business woman. Tell your sister to imagine her daughter introducing herself, when she's 24 and has graduated university or college and is at a job interview. Dr. Tennessee, Judge Tennessee, Lawyer Tennessee, Officer Tennessee do not sound at all professional, honestly.
Tell her that her daughter might not like the name because she thinks it's too out-there and not appropriate for a grown woman, and might want to change it, and actually name herself something else. Wouldn't your sister feel upset, at the least that she's put her own daughter through all the hardship?
If she doesn't agree to anything, and thinks that your over-reacting or is in denial :), then suggest that she gives her daughter 2 middle names, Tennessee January, and puts a first name in front of them. Middle names wouldn't matter as much, and she'd still get to name her baby Tennessee January, just with a name in front of them.
Good luck talking to her!
Hope I helped :)