How can a girl convey her desire to marry her maternal cousin to his family or hers without directly stating it, given her shyness and concern for her modesty?

There is no harm in a girl offering herself for marriage to her maternal cousin, provided Islamic guidelines are observed, and she can use her relatives as intermediaries for this purpose. Marriage is a destiny decreed by Allah, so one should not despair or lose hope if it is delayed, for Allah is Most Merciful and Most Knowledgeable of His servants' welfare. He may divert something they desire from them to store something better for them. Patience and good opinion of Allah are advised, for whoever fears Allah and is patient, Allah does not waste the reward of those who do good.