Is it permissible to either refer to or address a gentile priest as "Father XXXXXXXXX"?
What alternatives might there be?
Rav Berel Wein seems to feel it would be permitted to call a priest by the honorary title of "father":
One Motzei Shabbos (Saturday night), my Rosh Yeshiva, Rabbi Berel Wein shlita, was visiting a member of his congregation in the hospital. The patient was on the top floor and after the visit Rabbi Wein prepared to take the elevator down. The hospital has two sets of elevators, on opposite sides of the hall. As Rabbi Wein approached one elevator, he saw that standing at the opposite elevator was a Roman Catholic priest in full regalia. He too had just finished visiting one of his own parishioners and was leaving. The priest had just pushed the button for his elevator and Rabbi Wein proceeded to push the button for his elevator. Seeing Rabbi Wein still dressed in his Shabbos regalia, the priest looked over at him and said, "Good evening, Rabbi". Rabbi Wein turned and politely replied, "Good evening, Father." And then they both stood quietly waiting for the elevator to come. There were a number of people standing between the two clergymen. As they watched the proceedings they stood transfixed, as if paralyzed. They felt that the theological dispute of the centuries was about to be settled right before their eyes- which spiritual leader could command the first elevator. As Rabbi Wein would say, "Contrary to popular belief, G-d is on the side of Rabbis" and his elevator came first. The door slid open, Rabbi Wein smiled and magnanimously waved everyone in, including the priest. As the elevator began its descent, the priest looked at Rabbi Wein with a sly twinkle in his eye and remarked, "Rabbi, what would you have said if my elevator had come first?" Rabbi Wein replied, "Father, you can't prove anything from a descending elevator."