This is somthing that has come up time and again....
The bark will be in the best condition and easier to work with when taken from a living tree. Taking it from a living tree does not kill the tree as long as the inner bark is left intact, but will disfigure it and leave it vunerable to fungal infection. Where birch grows abundantly, there it always plenty of dead trees and the bark from these is perfectly usable for container making. It may be a bit more difficult to work so make sure you have a fire or some hot water to free up the resins in the bark to make it flexible. If you know of an area of trees that is being felled then this would be the best oppertunity to obtain 'green' bark.....although its a little late in the year to take bark from living or just felled trees.
In summary please please please try and use bark from dead trees or trees recently felled so to avoid unneccesary damage to the forest.
p.s. Pouring hot water on bark on dead trees will loosen it and make it easier to havest!
Hope this helps!