I don't know of any completely painless ways, but there is a fairly old way where you fill a bathtub with warm water and cut your wrists (deeply) and then you let them bleed while you relax in the warm water, the warm water helps combat the feeling of getting cold from blood loss and helps prevent your wounds from clotting, but doesn't do much else.
I don't recommend it though as it obviously can fail, and in order to bleed enough to actually pass you need to go fairly deep in order to make sure it's sufficient, and that'll hurt.