Is it permissible to pray for hidayah (guidance) of an infidel?

I have a friend, he does not believe in God. I believe that he is a good tempered person actually, so I want to make dua for his hidayah and faith. Is it permissible?

There is not any harm and objection in making dua for the hidayah (guidance) of a disbeliever, while it is not permissible to make dua for his forgiveness. So, you can’t pray for the forgiveness of your friend who is a disbeliever, however you can pray for his guidance and faith. The Prophet of Mercy (pbuh) invoked  the guidance for infidels.

The Blessed Prophet (pbuh) invoked not the wrath of God for the disbelievers, but their guidance

 Narrated Abu Huraira: At-Tufail bin 'Amr came to Allah's Apostle and said, "O Allah's Apostle! The tribe of daus has disobeyed (Allah and His Apostle) and refused (to embrace Islam), therefore, invoke Allah's wrath for them." The people thought that the Prophet would invoke Allah's wrath for them, but he said, "O Allah! Guide the tribe Of daus and let them come to us."  (Bukhari; 75; 406)

The Blessed Companion Hadrat Umar bin Khattab converted to Islam with the Prophet’s (pbuh) dua for his guidance

Hazrat Abdullah Ibn Abbas (rs) reported the Prophet (pbuh) as saying, “O Allah, strengthen Islam with Abu Jahl bin Hisham, or with Umar bin al-Khattab”. In the morning, Sayyidina ‘Umar (ra) went to the Prophet (pbuh) and accepted Islam; then prayed openly in the mosque. (Ahmad and Tirmidhi)

So, you can make dua for your friend’s guidance. Allah (swt) is the Merciful and All-Mighty who is the owner of hearts and owner of guidance. May He (swt) accept your duas in the best way.