Generic binary tree in C#
Here's an alternative way to write count().  It's shorter and uses expressions instead of statements.  You can't do as much in an expression, so I use them instead of statements when possible because there's a lower chance of things going wrong.  Readability is more important than those things, though, so I recommend using what is most readable to you.

private int count()
{
    return 1 +
        (_leftChild != null ? _leftChild.count() : 0) +
        (_rightChild != null ? _rightChild.count() : 0);
}


Or if you want to use C# 6 null checking:

private int count()
{
    return 1 + (_leftChild?.count() ?? 0) + (_rightChild?.count() ?? 0);
}


Method names should be UpperCamelCase, so count() should be Count().  I'm guessing you want to access a child's Count property instead of the method because the method is private.