Origin/Meaning of the title "The Blackcoat's Daughter"

As explained by the director Osgood "Oz" Perkins, son of Psycho star Anthony Perkins, in an interview with AV Club:

AVC: There’s been a lot of interest in the title being changed from February to The Blackcoat’s Daughter. Can you explain how all that went down, and the thought process behind the new title?

OP: For me, with the [original] title of February, I was going for the idea that a time can also be a location. In other words, you can re-visit a time of year, in the same way you can go back to a house that you used to live in. A certain month or a certain season can elicit a certain emotional response. That’s certainly true for anyone who has a negative anniversary on their calendar—the approach of that month brings the feeling of being very much back in another room. It’s a time that stands outside the rest of the year. So that’s where the title of February came from.

When the movie was bought by A24 to be distributed, I think they wanted a title that indicated the genre a little more strongly. I didn’t accept the alternate titles they were putting forth, so I went through [the film]. And I had a lot of suggestions, but I sort of landed on The Blackcoat’s Daughter. It’s a verse from this rhyme [for which] my brother Elvis wrote the music, and we used it as an incantation at the beginning and at the end of the movie: “Beetle beetle, blackcoat’s daughter, what was in the holy water?” I really liked the word “daughter,” and Elvis and I decided that maybe the backcoat’s daughter was a priest’s daughter. In any case, it worked for a priest, it worked for the devil, it worked for a father, it had the quality of a child raised by this strange black coat. It felt sexy enough.