If the config JSON is stored as a static file and used over and over, a clean solution would be to simply remove the quotes from around the function(s) in the JSON and then do this:
var get_config = eval("(" + json_data + ")");
The JSON needs to be wrapped in parenthesis to evaluate, that's why you're getting the error. If the config JSON is constantly needing to be stringified then there's a couple of other options. You could do this to call the function:
var get_config = eval("(" + json_data + ")");
eval("(" + get_config.afunction + ")")("this is passed to the function");
or you can use the JSONfn plugin (http://www.eslinstructor.net/jsonfn/) to stringify the JSON instead of the functions you're using and just eval it like above. The JSONfn plugin is able to serialize functions like you're needing to do.
Here's a jsFiddle to mess with that shows the above code in use: http://jsfiddle.net/4UP53/