The Scriptures teach that God never gives us more to bear than we can handle. There is no place for euthanasia in Christianity. Read "the book."
On the other hand, if someone who is not Christian wants to end their life, who are we to say they must follow OUR belief of God? Have you witnessed to them? Have you explained our great Savior?
This is the problem I have with "social" conservatism and why I lean libertarian anymore. I believe it my duty to change hearts one at a time. It is not my government's job to mandate Christianity.