Ruling on reading Qur’aan over graves, and saying du’aa’ for oneself at the graveside

Reading the Holy Qur’aan at the graveside is bid’ah. It was
not narrated from the Prophet (peace and blessings of Allaah be upon
him) or from his companions. As it is not narrated from the Prophet
(peace and blessings of Allaah be upon him) or from his companions, then we
should not introduce it by ourselves, because the Prophet (peace and
blessings of Allaah be upon him) said, according to a saheeh report: “Every
introduced matter is an innovation, and every innovation is a going astray,
and every going astray will be in the Fire.” What the Muslims must do is to
follow the example of the earlier generations, the Sahaabah and those who
followed them in truth, so that they will be following goodness and true
guidance, because it is proven that the Prophet (peace and blessings of
Allaah be upon him) said: “The best of speech is the Book of Allaah and the
best of guidance is the guidance of Muhammad (peace and blessings of
Allaah be upon him).” 

As for saying du’aa’ for the deceased at the graveside, there
is nothing wrong with that. A person may stand at the graveside and say
whatever du’aa’s he can, such as saying, “O Allaah, forgive him; O Allaah,
have mercy on him; O Allaah, admit him to Paradise; O Allaah, make his grave
spacious” and so on. 

With regard to a person saying du’aa’ for himself at the
graveside, if he does it deliberately then it is also an innovation
(bid’ah), because no place is specified as a place for du’aa’ unless there
is a text concerning it. If there is no text concerning it and no Sunnah has
been narrated concerning it, then that – i.e., singling out a place for
du’aa’, no matter what the place is – is a bid’ah. End quote. 

Majmoo’ Fataawa Ibn ‘Uthaymeen
(17/228) 

For more information please see the answer to question no.
36513. 

And Allaah knows best.