How do you say "Don't cry. Everything will be alright!" in Japanese?
there are no details, really. That's just it!

Question

Answer

Don't cry=泣かないで(nakanaide)
Everything will be alright!=大丈夫だよ！(daijoubu dayo)←this is difficult ;^^

Answer

Well, Hikaru did gave you a good answer, but  I would say this:

Don't cry. ( Nakanaide)
Everything will be all right. ( なんとかなるよ）　Nantoka Naruyo
It means, "Just let it flow and let's see."