If the MC, as the territory lord, hasn't got personal funds to developed the land, despite the land offering rich mineral resources, the answer is to go capitalist on it. Form a public company and have rich, interested merchants invest in it. If the kingdom really has no interest in defending the place from constant raids from the neighbouring country, then bloody switch allegiance over to that neighbouring country. Obviously they do have the means to keep sending the military there. Seriously, though, if successful, productive mines were to be established, the king ought to become interested, as it's a matter of national importance.