Is there a way to make readonly (not just private) automatic properties?

Question

Automatic properties let me replace this code:

private MyType myProperty;
public MyType MyProperty
{
    get { return myPropertyField; }
}

Answer 1

No, unfortunately not. I would very much like the feature, which could look like this:

public readonly string Name { get; }

or (slightly oddly)

public readonly string Name { get; readonly set; }

This would be converted into something like:

private readonly string <>_Name;

public string Name { get { return <>_Name; } }

The twist is that setter calls would be allowed - but only within the constructor. Such calls would be converted directly into assignments to the backing field.

I would dearly, dearly love such a feature. Maybe for C# 5...