Enough MBTI, can we talk Enneagram in regards to these beloved characters? Here are my educated guesses, I've added explainations to some for why I typed them as I did.
Upstairs
Violet Crawley - 1 or 6. We know that she's s traditionalist, but is it because "it's right" or because "it's safe"?
Robert Crawley - 6w7. He is all about the authority of the noble class, and fearful of it's passing. Responds in a counter-phobic way in many situations, especially in regards to politics, and change (which he is fearful of). He also seems to feel a large amount of responsability to his ancestors and family in his efforts to save Downton.
Cora Crawley - 9w1. Constantly a peacemaker in the household, and very rarely engaging in conflict of her own. She's very calm under pressure and is involved in several emergency situations that reveal her calm nerves and quick mind. Charming in an agreeable way, I believe she displays integration to 3 pretty regularly in the show. Her 1 wing comes in to play in the way she has handled deceit or wrongdoing in her household with servants, with firm and decisive action.
Mary - 3w4. Image focus, desiring to be the best in a variety of ways, and willingness to be false and deceive where necessary. The exchange between her and Mabel Lane Fox in a recent episode (s5, e6) is a great example of this-- Mary says she is dying to ride astride in the horse race, and Miss Fox asks why she doesn't. "Not in front of my Grandmother" (image, appearing to be what she's not. Forsaking the "heart's desire"). Mabel says she surprises her and that she seems to know just what rules she's willing to break, and what not. Also the comment in this episode that she doesn't "believe in letting others win."
Edith - 4w3 So/Sp. Sees herself as a suffering victim, largely disintegrating to 2 much of the series. Feels inherently different than her sisters and that they (and everyone) have all the happiness she never will. A couple of scenes in which she and Branson bond over their differentness come to mind. She is very sensitive, often having her feelings hurt and storming out in a huff (dramatic). Her healthiest moments come when expressing herself through writing, and standing on her own two feet through her career.
Sybil - 9w8 Sx. Calm, gentle and intuitive but also firm, action oriented and not afraid to break the mold.
Rose McClaire - 7w8 So/Sx. Spontaneous and carefree, sometimes to the point of recklessness. One of the characters in the show who is thrilled about change and is fully immersed in it. Her 8 wing is most visible through her vengeful feelings towards her mother, and her fearless independence.
Aunt Rosalind Crawley - 1w2. Rigid and tends to respond with defensiveness and anger. Appalled by anything morally unsound or lack of adherence to decorum-- Rose's outing to a speakeasy while in London, Edith's pregnancy, etc. Counts herself as an authority, even to a hypocritical extent (telling Edith what to do in regards to her child, though she has never been a mother herself).
Matthew Crawley - 7w6. Often healthily integrating to 5, Matthew has a head for business and law. Comfortable with change and entertaining different perspectives (variety), he often takes the more progressive stance.
Isabelle Crawley - 1 or 8?
Thomas Branson - 8w9. Coming from an unjust and humble Irish background, his survival instincts have always been necessary. He is direct with his opinions and feelings but has a kind heart. As the series goes, his integration to 2 becomes much more apparent as his relationship with the Crawleys becomes more affectionate and less of a power struggle.
Downstairs
Carson - 1w2
Mrs. Hughes - 6w5. She is always in the know about everything, prepared for the worst and shows deep love and compassion for those she works with. One of the most loyal to the family of our downstairs characters, and also to her family-- as we later learn she uses all of her income to support her ill sister. Her five wing is pretty apparent in her observation skills, and gift for discretion. She tends to put two and two together quickly.
Mrs. Patmore - 2w1. Self sacrificial towards others, picking up work so others can go on outings, etc. but often during meal preparations reminds everyone who is doing all the work (her).
Thomas - 3w4 his main goal is to win, and he will do anything to achieve it. He resents his social class and is a true ladder climber, trying to get in the good graces of the Lord and Lady at any opportunity (but thinking I'll of them behind their backs). He's also very deceitful, lying more times than we can count to put others in a dark light, or trick others into doing things that hurt them in the end. He is deeply wounded, and full of shame over his sexual identity-- sometimes reveling in this, other times desperate to change himself to be "like other men".
John Bates - 5w6. Extremely observant and intelligent, skilled in a variety of ways that have developed to ensure survival (integrating to 8)-- forgery, slight of hand, and general knowledge of others and his surroundings.
Anna Bates - 9w1. Generally calm and caring to those around her, serves practically as Mary's therapist. Disintegrates to 6 under stress in the rape plotline, becoming passively fearful and anxious.
Daisy - 6w7. Reactive and free with her opinions. Loyal to those she likes, and judgmental prickly to those she doesn't. Naive at times.
Mr. Mosley - 7w6. Goofy, dissatisfied but resigned to a life in service out of loyalty to his family (to support them).
Miss Baxter - 5w4. Both shame filled and and self loathing, empathetic but strong emotionally. She's also ridiculously observant, this gift is the reason Thomas brings her to Downton to begin with.