There's nothing in Fiddler/FiddlerCore itself that will do this. You can easily start the process from a Firefox extension (see overlay.js in Fiddler's install folder):
var certdb = Components.classes["@mozilla.org/security/x509certdb;1"].getService(Components.interfaces.nsIX509CertDB);
var file = Components.classes["@mozilla.org/file/directory_service;1"].getService(Components.interfaces.nsIProperties).
get("Desk", Components.interfaces.nsIFile);
file.append("FiddlerRoot.cer");
try {
alert("On the following screen, tick the first checkbox: 'Trust this CA to identify websites.'");
certdb.importCertsFromFile(null, file, Components.interfaces.nsIX509Cert.CA_CERT);
} catch (e) { alert("Trust function returned:\n\n" + e); }
From outside Firefox or to bypass all prompts, you'd need to poke their API; see e.g. How to add a trusted Certificate Autority to Firefox with JSS shows one approach.