Making a superclass have a static variable that's different for each subclass in c#

There is a more elegant way. You can exploit the fact that statics in a generic base class are different for each derived class of a different type

public abstract class BaseClass<T> where T : class
{
    public static int x = 6;
    public int MyProperty { get => x; set => x = value; }
}

For each child class, the static int x will be unique for each unique T Lets derive two child classes, and we use the name of the child class as the generic T in the base class.

public class ChildA: BaseClass<ChildA>
{
}

public class ChildB : BaseClass<ChildB>
{
}

Now the static MyProperty is unique for both ChildA and ChildB

var TA = new ChildA();
TA.MyProperty = 8;
var TB = new ChildB();
TB.MyProperty = 4;

While this works fine, I'm wondering if there's a more elegant or built-in way of doing this?

There isn't really a built-in way of doing this, as you're kind of violating basic OO principles here. Your base class should have no knowledge of subclasses in traditional object oriented theory.

That being said, if you must do this, your implementation is probably about as good as you're going to get, unless you can add some other info to the subclasses directly. If you need to control this, and you can't change subclasses, this will probably be your best approach.

This is a little different than what you're asking for, but perhaps accomplishes the same thing.

    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine((new B()).theValue);
            Console.WriteLine((new C()).theValue);
            Console.ReadKey();
        }
    }

    public abstract class A
    {
        public readonly string theValue;

        protected A(string s)
        {
            theValue = s;
        }
    }

    public class B : A
    {
        public B(): base("Banana")
        {
        }
    }

    public class C : A
    {
        public C(): base("Coconut")
        {
        }
    }