Can we type characters, too? In this case, I'm referring to the first season.
My opinions:
Constance - ENTJ. A lot of people claim she's an ENFJ or ESFJ, but that would mean she has a lot of Fe which, IIRC, there was almost none of.
Tate - INTJ. He seeked to have control over others which makes me think he was an underdeveloped Judger, and wanted to protect Violet. He would talk to Violet (someone he was very close to) about his feelings but didn't care much about anyone else's (Fi?) and often kept his knowledge to himself (Ni,) though I might only be saying that because he intentionally didn't tell Violet she was a ghost. He came off as introverted to me, except with Violet whom I also believe was an introvert.
Violet - ISFP. I think I saw a lot of introversion and perceiving. Like with Tate, she also wasn't very open with her emotions (Fi) but did confide in him. I didn't notice a strong use of Intuition.
Vivien - ISTP
Moira - ISFP, maybe.
Ben - ISFJ(?)
Larry - Ugh..really don't remember him much. But if I had to venture a guess, I'd say INFP.