Create Instance using base constructor

If I understand it correct you can't modify ExampleClass but need to create an instance of it that uses a different constructor for the base class?

I belive there is not build in way in the framework to achive it, even with reflection. So your goal should be to bypass the framework and use MSIL

However, this topic I found on SO looks promissing.

Dynamically create type and call constructor of base-class

Do you want to call the base class' constructor?

public ChildClass(string arg1) : base(arg1)
{
    //above will invoke base constructor that takes a string argument
}

The only way I can see to do this is to add a ParentClass constructor. I doesn't have to do anything, so I don't see why you can't add it:

public ParentClass(string argument1) : BaseClass(argument1)
{
}

Try this:

class ExampleClass : BaseClass
{
    public ExampleClass()
        : base(Properties.Settings.Default.MyArgument)
    {
    }
}

You can use Properties.Settings.Default.MyArgument in order to pass in the value of the argument you want use in the base class constructor without modifying the source code everytime the argument's value needs to be changed (just add it into the projects's Settings, application scoped).

If you can't add a non-default constructor to your ChildClass, then no you can't create an instance of ChildClass calling a base class constructors. Constructors are not inherited. What you need to then is to refactor your base class so that there is way to set the argument not using a constructor. For example see below:

class BaseClass
{
    public BaseClass()
    {

    }
    public BaseClass(string argument1)
    {
         Init(argument1);
    }

    public void Init(string argument1)
    {
        //...
    }
}

class ExampleClass : BaseClass
{
    public ExampleClass()
    {
    }
}

Then you can create an instance of your ExampleClass and call the Init method to initialize it:

 ExampleClass e = (ExampleClass)Activator.CreateInstance.... // or whatever
 e.Init(arugment);