What can I do about a neighbor's baby crying and keeping me awake?
Wow, tough question.
If it were a barking dog, you'd have a good "private nuisance" case - when something or someone is interfering with your quiet enjoyment of your property. In the case of a crying infanty, that is a lot more difficult, though still possible in theory. The trick would be finding a lawyer who would take your case. Sellers and Landlords are prohibited from discriminating against families with children. That's a big roadblock. It's still possible that you could sue the landlord for private nuisance, with the remedy being moving the family to a condo further away from yours (assuming an empty one is even available). But I am thinking this is a long shot.
Most likely, there is very little you can do, legally. But if you haven't already tried, there are some really good soft ear-plugs that you could wear while sleeping. They are soft foam that you squeeze down, insert into your ear, then they expand to fill your external ear canal. Go to any hunting store or the hunting/guns area at Walmart, etc. Ask for foam earplugs and they'll show you. Very cheap. You don't even feel these things in your ears when you're wearing them. You'll be used to them in no time. In your situation, I think they'd be worth a try. Longer term, at least (most) babies start to sleep through the night before they are one year old. So your problem may solve itself before long.