I'm going to take a stab at this, and I haven't read any of the other posts. First, the prisoners have to appoint a counter. Next, the strategy has to be that the first K+1 times (where K = no. of times the King can touch the chalice) a non-counting prisoner enters the chamber and the chalice is up, they have to put it face down. If they enter the chamber and it's face down, or if they have already changed it to face up K+1 times, the non-counter will not touch the chalice. The counter's job will be to always change the chalice from face down to face up, and to count how many times he's done this. Once he has counted up to K+ N (N = total prisoners), he will know that all of the prisoners have entered the room. The first 1 is necessary because it's possible that the counter will be the first person into the room, and the chalice will start face down.

For example, if the king could mess with the chalice twice, and there were only 3 prisoners (a,b,c) and a was the counter, a possible sequence could go like this:

b enters and chalice is down
a enters, turns chalice up (1)
b enters, turns chalice down (1)
c enters
a enters, turns chalice up (2)
b enters, turns chalice down (2)
King enters, turns chalice up (1)
b enters, turns chalice down (3)
a enters, turns chalice up (3)
c enters, turns chalice down (1)
King enters, turns chalice up (2)
a enters
c enters, turns chalice down (2)
b enters
a enters, turns chalice up (4)
c enters, turns chalice down (3)
a enters, turns chalice up (5), and tells the king they've all been to the room.