To generate this property I guess you are using the prop template
So you can either change it, or create a new one of your own
Go to ReSharper Menu -> Templates Explorer
Choose C# and look for prop , you can click edit and change it
But maybe the best way is to create a new one if you sometimes want default properties
Click new template and write that
protected $TYPE$ $NAME$ { get; private set; }
In the shortcut field type what you want, like prprop for example and save it.
Now open a file and type prprod, tab twice and you got the protected propertiy with private setter
If you are not using templates or snippets but the "Create auto-property from constructor" it seems it's impossible to change the access modifier, the only way to change it is when you use
Resharper -> Edit -> Generate Code ...
Then from there what you choose to generate you can change access modifiers or choose if it's read only.