Jesus says there is only one unforgiveable sin.

That is blasphemy of the Holy Ghost. Besides that all sins can be forgiven through Christ.

If someone is truly a Christian then they will be committing a great sin against God by killing themself. They will be detroying the life God has entrusted to them. They will be doing this while knowing they are wrong.

This is a great and horrible sin but it is one that God can forgive in his mercy.