All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
We don't know any specific supplication on this matter, but you can make supplications that invoke Allah, the Exalted, to make difficult matters easy to you based on the Hadith narrated on the authority of Anas ibn Maalik that the Prophet said, “O Allah, there is no ease other than what You make easy. If You please You ease sorrow.” [Narrated by Ibn Hibbaan in his Saheeh] Al-Hafidh ibn Hajar on his part, classified this Hadith as authentic. Also, Imam Ahmad and Imam At-Tirmithi among many others, narrated on the authority of Saʿad that the Prophet said: “The supplication of Dhun-Nun (Prophet Younus) when he supplicated, while in the belly of the whale, was: ‘There is none worthy of worship except You, Glory be to You, Indeed, I have been of the transgressors.' So, indeed no Muslim man supplicates with it for anything, ever, except Allah responds to him.”
However, in case this girl had embraced Islam and duly observes its commands and keeps away from its prohibitions, you are allowed to get married to her. But, if she is still a polytheist, you are prohibited from doing so – a fact recorded in the Saying of Allah, the Exalted (which means): {And do not marry polytheistic women until they believe. And a believing slave woman is better than a polytheist, even though she might please you.} [Quran, 2:221] We seize the opportunity to call your attention to the fact that some women might sometimes pretend to have embraced Islam for the sake of marrying from a certain man, yet they are not Muslims.
Regarding your family’s objection to your marriage from this woman, it is impermissible for them to do so merely because she belongs to a Hindu family, especially you stated that she had embraced Islam and duly observes its commands and keeps away from its prohibitions. So, you can continue trying to convince them; if you managed to do so, you have – praise be to Allah – achieved your goal. But, if your parents insist on rejecting this marriage, showing obedience to them is given precedence over that marriage. This would be the ruling unless you are afraid of committing a sin with her, in which case it is permissible for you to marry her without their consent, but you should strive doing your best to be dutiful to them and gain their consent afterwards. For more information, consult Fatwa 84942.
Allah knows best.