Is it permissible to propose to a girl one is fond of without the knowledge of the father who rejects her and wants to marry his son to his paternal cousin's daughter?

Obedience to parents is obligatory in matters that do not involve disobedience to Allah and are within what is considered good and proper. If parents forbid marriage to a specific woman for a reasonable cause, then obedience to them becomes obligatory, because obedience to them is a duty, whereas marrying that particular woman is not. However, if the father absolutely forbids his son from marrying at all, or wishes to compel him to marry a woman he does not desire, then there is no obedience to him in such a matter. Thus, if the father's rejection of the girl you have proposed to is an absolute rejection of any girl other than the one he designates, and not for a reason specific to the girl herself, then obedience to him is not obligatory. Yet, if the girl whom the father has proposed (for his son) possesses good character and religious devotion, then it is advisable to accept her and comply with his command in that regard.