EDIT: Thanks to New xDante1986 for pointing this out: the bible only appears during Taylor and Daniel's trip through the museum. John and Andrew have a completely different book on the table.
During either group's time in the museum, look for the bible on the table and open it to find devilish symbols/writing. This should give you the option at the end in the courthouse to accuse Carver, with proof, and have Mary saved.
There could be other ways to unlock this, but this is what worked for me. Abraham will tell the judge to check the bible, where he will see the symbols, and have Carver arrested.