We should know that during menstruation, women can read the Qur’an and makedhikr (remembrance of Allah) and du`aa (supplication), though they are forbidden from fasting, performing salah (Prayer) and touching the mushaf (copy of the Qur’an). In this way, they still have the opportunity to engage in dhikr and du`aa’ while menstruating.

As for visiting a graveyard, there nothing wrong in it. An Islamic scholar, Sheikh Ahmad Kutty, said in his response to question of this as follows:

“You are certainly allowed to engage in dhikr and du`aa while menstruating. As Imam Nawawi pointed out, there is a virtual consensus among scholars and jurists that both men and women in a state of sexual defilement (janabah) and women while menstruating or undergoing a postpartum period of bleeding can make dhikr either through spoken words or silently in their hearts.

It is also permissible for them, while making supplications, to use the familiar du`aa’s that are taken from the Qur’an such as the following:

(Our Lord, grant us true joy in our spouses and children and make us role models for those who are mindful [of You]).
Rabbanaa aatinaa fid-dunya hasanatan wa fil-aakhirati hasanatan wa qinaa adhaaban-naar. (Our Lord, grant us good in this world and good in the next world and save us from the torments of the Hellfire).

Rabbanaataqabbal minnaa innaka antas-samee`ul-`aleem wa tub `alaynaa innaka antat-tawwaabur-raheem (Our Lord, accept this work of ours, for verily You are All-Hearing, All-Knowing; and grant us repentance, for You are the Relenting, the Merciful).”