If someone has ask Allah to give him a boy then he will make him Hafiz-e-Quran and then the boy has been given by Allah to him and if he does not make him Hafiz-e-Quran then is there any kaffarah for him.
بسم الله الرحمن الرحيم
It is not wajib to fulfil this vow (mannat) and there is no kaffarah on him. However, if he makes him memorize some verses of the holy Quran then it shall also suffice.
Allah knows Best!
Darul Uloom Deoband