To get the mark, you need to sleep for a random amount of time (can be at least an hour real time) in northeastern of the four Peaceful Bliss rooms (dizzy/NPK) in the Temple of Vandyne, you will need to be levitating and visible. Once you obtain the mark you will need to either dispel area the room to safely exit into NPK and leave, or simply pray death. Having a friend watch while you try this mark during the daytime is best. This mark seems to previously only be given in the northeast Peaceful Bliss room, though has been verified in 2019 to work in the southeast Peaceful Bliss room also.
2019 Update - Tutorial Quest
This mark is now granted through tutorial quest #3205. Rewards text for archon class:
You have been granted the Mark of Serenity! You receive 0 quest points, 20 archon points, 5 piety, and 43 practices.
For patiently seeking enlightenment within this chaotic world, the Powers have granted thee a mark. You have been granted the Mark of Serenity! You gain 315,000 experience points! You gain 36 practices! You gain 6 piety!