The 6th Ammendment "In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence." I would think it implies a fair trial also, but it doesn't explicitly say it.
The 1st Ammendment "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof..." I would think that if one was capable of seeing the implication of a fair trial in the sixth, he would easily see the implication of seperation of church and state in the first.
But on the other hand, sometimes I do give people too much credit.