Dorothy - ENTJ
She always looks for a logical answer in things. Whenever any of the girls or herself has a problem, she knows how to deal with the situation logically. She prefers to act upon these thoughts too, making her Te. She always has to confront a problem too. She's never afraid to share her honest thoughts toward something. Sometimes she can be thought of as rude, because her opinions rarely consider the sensitivity of others. Like most Js, she can also get mad when things do not go her way. However, emotional concerns rarely appear for her. Out of all the girls, I've only seen her cry once, but that was only because she had fatigue, traveled to many doctors and didn't believe she was sick. Who wouldn't cry? There was also an episode where she said that she had problems confronting her feelings (also implying that she inherited it from Sophia). I'd suspect that she is also an Ni auxiliary, because she's always telling Rose in her stories to get to the point. She is also rarely prone to care about her personal space (Si) and more interested in concepts. But ESTJ wouldn't be far off either.
Blanche - ESFP
Blanche is a typical live in the moment person. She is always interested in new sensational activities such has having fun on nights out and going to men's houses. Blanche always wants to try new things like auditioning for a play. As a kid she also did a lot of pranks too just for the sake of the sensational experience herself. She is often concerned with her looks, which hints more to the sensational element of her "sexual persona". But she can also genuinely have a concern for feelings too. It is a more personal sense of feelings though. When her father dies, she doesn't react to the situation until she puts her own feelings into it. Also, when she discovers her brother is gay, she does not understand it at first, but begins to accept him until she can relate her personal feelings to the situation (Fi). Rarely does judgment ever come into question. Sometimes Dorothy points out when she is in a bad relationship, but Blanche prefers not to judge and likes living in the moment. She proves the ESFP type to be the ones known for putting on a show.
Sophia - ENTP
She has a very witty sense of humor that is based on these far-fetched ideas. Sometimes when she tells a story she is lying, but they quite creative. And comes up with ideas right on the spot. In times of emergency, she can always be relied on for her innovative ideas. But is less likely to use Se, because you can tell that she is far more "out to lunch", thus less living in the sensational moment. There is also a typical ENTP side of her that comes up with business schemes rooted from her Ne and Ti. There was an episode where Dorothy mentioned how she used to try and sell some whacky products. Sometimes she gives the other girls good advice, when she isn't lying. A lot of her advice is based on her Ti. Generally, Sophia tends to be less personal and can sometimes be a bit mean and a prankster to others (ex. getting revenge from her friend Gladys). But her Fe side can be quite evident too. When she is offended by someone she will react quickly to them and less likely to spend time reviewing it over. In contrast, it is clear that Blanche and Dorothy can hold longer grudges or "go to their room".
Rose - ENFJ
Rose is known for her highly optimistic attitude. She constantly tries to maintain a state of happiness, which is quite involved with her and others. Despite other character's outlook on her, she is the most willing to help others. She is always concerned if she might offend someone, because her Fe dictates that she tries to maintain a state of happiness with herself and environment. Sometimes her cheery spirit can go away, because her Fe reacts to negative things too. In an episode a pessimistic lady, Mrs. Claxton kept interuptting her in her plan to save a tree. She got very angry at her. But later was sad that her anger possibly lead to Claxton's death. There are times when she has problems understanding things, because she supresses her Ti and is more likely to rely on concepts on her own Ni. In one episode, she conveyed a certain ideology toward saving manatees and she is generally cought up with community ideals. She is most involved in the community activities most likely because she has an image toward society (Ni). She also uses her Ni frequently to reflect on past experiences such as her life in Saint Olaf.
I suspect that Stan is an ENFP, but he hasn't had enough appearances for me to judge.