Where can I get a free online copy of the script of The Amen Corner?
If you manage to find a free online copy of this play, it is there illegally. The Amen Corner was published in 1955. Copyright laws protect it for the lifetime of the author plus 75 years. Since James Baldwin died in 1987, that means the play will be under copyright until the year 2062. Until then, anyone who wishes to publically reproduce more than two lines of the play must have the written permission of the heirs or estate of James Baldwin.
You must remember that the plays, novels, stories, etc., that writers produce are their livelihood. They are paid royalties for each copy that someone buys. If you bypass the purchase, you rob the author or his heirs of their income. If you want a copy of the play, you're going to have to pay for it.