What was the Church actively doing to help the process of integration in Warriors Don't Cry?

The white supremacist Governor of Arkansas, Orval Faubus, orders the National Guard to enforce segregation at Little Rock High despite its being ruled unconstitutional by the Supreme Court in Brown v. Board of Education. In response, some members of Melba's church form a group with people from other churches. The group will pray and work for peace in the city as well as offering whatever support they can to Melba and the other students.
One of those students is Ernest Green, the oldest of the Little Rock Nine and a member of Melba's church. Indeed, all of the Little Rock Nine are active members of their local church. The church provides moral support for all the students, praying for them and being there for them whenever needed.
The deeply devout Grandma India believes that Melba and the other students have been given an assignment from God and they must carry it out, however difficult that may be. She chides Melba when she seems on the brink of giving in and encourages her to greet every attack she receives at school with a smile and a thank you. Grandma India's advice neatly encapsulates the passive nature of the church's resistance to segregation.