du`a for guidance of someone close
Question

what would be a good du'a or ayah to recite if you want Allah to open the heart of someone very close to you to Islam?
Praise be to Allah.The best thing to do in this situation is to pray for guidance for that person. This is what the Prophet (peace and blessings of Allah be upon him) did, as is reported in a number of ahadith, such as the following:
Abu Hurayrah (may Allah be pleased with him) reported that Tufayl ibn Amr al-Dawsi and his companions came to the Prophet (peace and blessings of Allah be upon him) and said: O Messenger of Allah, Daws have rebelled and disobeyed, so pray to Allah against them. People said, Now Daws are doomed! He said, O Allah, guide Daws and bring them here.
(Reported by al-Bukhari, 2937).
Abu Hurayrah said: I was calling my mother to Islam, when she was still a mushrik. One day I called her to Islam and she said something about the Messenger of Allah (peace and blessings of Allah be upon him) that upset me. I came to the Messenger of Allah (peace and blessings of Allah be upon him), weeping, and said: O Messenger of Allah, I was calling my mother to Islam and she refused. Today I called her and she said something about you that upset me. Pray to Allah to guide the mother of Abu Hurayrah. So the Messenger of Allah (peace and blessings of Allah be upon him) said: O Allah, guide the mother of Abu Hurayrah. I left, feeling hopeful because of the Prophets prayer. When I got home, as I came near to the door I saw it was ajar. My mother heard my footsteps and said, Stay where you are, Abu Hurayrah! I could hear the sound of water. She washed herself, got dressed and put on her khimaar (head covering). Then she opened the door and said, O Abu Hurayrah, I bear witness that there is no god except Allah, and I bear witness that Muhammad is His slave and Messenger. I went back to the Messenger of Allah (peace and blessings of Allah be upon him), weeping with joy, and said, O Messenger of Allah, good news! Allah has answered your prayer and has guided the mother of Abu Hurayrah. He praised and thanked Allah, and said, That is good. I said, O Messenger of Allah, pray to Allah to make my mother and me dear to His believing slaves, and to make them dear to us. The Messenger of Allah (peace and blessings of Allah be upon him) said, O Allah, make this slave of Yours (meaning Abu Hurayrah) and his mother dear to Your believing slaves, and make the believers dear to them. There is no believer who hears of me or sees me, but he loves me.
(Reported by al-Bukhari, 4546).
Jaabir said: They said, O Messenger of Allah, we have suffered much from the arrows of Thaqeef (this was when they were fighting, before they became Muslim), so pray to Allah against them. He said, O Allah, guide Thaqeef.
(Reported by al-Tirmidhi, who said: this is a hasan saheeh ghareebhadith. Sunan al-Tirmidhi, no. 3877).
We ask Allah the Most Generous, Lord of the Mighty Throne, to guide your loved one to Islam soon, by His Grace and Mercy. Allah is the One Who guides to the Straight Path.