I imagine you could do even better with something like PostSharp or Fody.

    public void MyFunction([InRange(0, 5)] int x, [NotNull] object y)
    {
        // ...
    }

I just checked, and in fact Fody can do something just like this [1].

The only downside I see is contracts like this would be hard to write concisely:

    if (useFirstObject == true)
        Contract.AssertNotNull(firstObject);
    else
        Contract.AssertNotNull(secondObject);

[1] https://github.com/Fody/NullGuard