Without a setter, you would never be able to provide a value - as you don't have any way of specifying the backing variable's name.
I've requested a readonly automatic property, declared like this:
public string ReadonlyProperty { get; readonly set; }
which would create a readonly backing variable, a property with only a getter, and translate all calls to the setter into direct access to the variable. You could only call the setter within the constructor - just like for normal readonly variables.
We'll see whether this request does any good... it's a real shame it's not in there at the moment, as it makes it harder to implement immutable types than mutable types :(