Is there a prayer that can ensure that a person will become a Muslim?
Any prayer can be read for it. What matters is the prayer based on deeds in the first place. We should practice Islam and serve as good examples. Then, it is necessary to tell a person about Islam taking into consideration his state, environment and needs. It will be nice to pray for that person after that.
According to a narration, the Messenger of Allah (pbuh) said, “O Allah! Strengthen Islam with either of these two men – Abu Jahl and Umar b. Hattab – ” The Messenger of Allah (pbuh) added the following : “The more beloved of them in the sight of Allah was Umar.” (Tirmidhi, Manaqib, 18; see Musnad 2/25; Qadi Iyad, ash-Shifa, 1/327; Bayhaqi, Dalailu’n-Nubuwwa, 2/215)
We can say a prayer like this: “O Allah! Make this person a believer; make him embrace Islam.”