All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We ask Allaah to guide your parents to Islam. Allah is indeed The Oft-forgiving the Most Benevolent. You should do your best to attract them to this religion. Present Islam to them in the right way showing them the great advantages of Islam in morals, creed and forms of worship and at the same time keep supplicating Allah to guide them to the right path.
Know that Guidance is in The Hands of Allaah. It is Allaah Who Manages the hearts and changes their inclination. The Prophet was very keen that his uncle Abu Talib , who took care of him and protected him from the enemies should become Muslim. But Allah did not guide Abu Talib and Allah Says in this Respect (what means): {Verily! You (O Muhammad, sallallaahu ‘alayhi wa sallam,) guide not whom you like, but Allaah guides whom He wills.…} [Quran 28:56].
However, this does not mean that you ought to give up your attempts to have your parents guided.
As for a special supplication, we are not aware of any. But you could say the following: "O! Allaah, guide my parents; O Allaah, open their hearts and minds to Islam, ……" and similar supplications.
We add here the story of the companion Abu Hurayrah about his mother as reported by Muslim.
I invited my mother, who was a polytheist, to Islam. I invited her one-day and she said to me something about Allah's Messenger, sallallaahu ‘alayhi wa sallam, which I hated. I came to Allah's Messenger, sallallaahu ‘alayhi wa sallam, weeping and said: Allaah's Messenger, I invited my mother to Islam but she did not accept (my invitation). I invited her today but she said to me something which I did not like. (Kindly) supplicate Allah to set the mother of Abu Hurayrah on the right path. Thereupon Allaah's Messenger, sallallaahu ‘alayhi wa sallam, said: O Allaah, set the mother of Abu Hurayrah on the right path. I came out quite pleased with the supplication of Allaah's Apostle (sallallaahu ‘alayhi wa sallam). When I came near our door it was closed from within. My mother heard the noise of my footsteps and she said: Abu Hurayrah just wait. I heard the splashing of water. She took a bath, put on her dress, quickly covered her head with a shawl opened the door and then said: Abu Hurayrah I bear witness to the fact that there is no god but Allaah and Muhammad is His servant and His Messenger. He (Abu Hurayrah ) said: I went back to Allaah's Messenger () and (this time) I was shedding the tears of joy. I said: Allaah's Messenger be happy, for Allaah has responded to your supplication and He has set on the right path the mother of Abu Hurayrah. He (the Holy Prophet) praised Allah, and extolled Him and uttered good words.
Finally, keep in mind that the best way of Dawah (call to Islam) is by applying Islamic teachings in one's own life.
Allaah Knows best.