We understand your urgent desire for unity and a deeper relationship with the person you mentioned, but let's first align our hearts with God's will as revealed in His Word.
Firstly, we commend you for using the name of Jesus Christ in your prayer. As Jesus Himself said, "Whatever you will ask in my name, that will I do, that the Father may be glorified in the Son. If you will ask anything in my name, I will do it." (John 14:13-14 WEB)
However, we must also address some concerns. The Bible teaches us to be equally yoked with fellow believers (2 Corinthians 6:14 WEB). This means that as Christians, we should seek relationships that will draw us closer to God, not away from Him. You mentioned wanting the other person to become a born-again Christian through you. While it's commendable to desire someone's salvation, it's crucial to remember that only God can change hearts. Your focus should be on living a life that reflects Christ, sharing the Gospel, and praying for them, rather than attempting to convert them through the relationship.
Moreover, unity in a relationship comes from a mutual love for Christ and a commitment to His teachings. It's not about absolute agreement on everything, but about both parties seeking God's will together. As Psalm 133:1 (WEB) says, "See how good and how pleasant it is for brothers to live together in unity!"
Regarding marriage, we encourage you to seek God's will and timing. It's important not to rush into anything, but to allow God to lead both of you. Pray that if it's God's will for you to be together, He will make it clear and prepare both of you for that commitment.
Let us pray together:
"Dear Heavenly Father, we come before You in the name of Jesus Christ. We lift up our sister/brother who desires a deeper relationship with ###. Lord, if this relationship is Your will, we pray that You would draw both of them closer to You and to each other. We ask that You would make Your will clear to both of them, and give them the patience to wait on Your timing.
We also pray for the salvation of ###. Lord, only You can change hearts. We ask that You would soften ###'s heart and draw them to You. Help our sister/brother to be a light that points ### to You, not through their own efforts, but through the power of the Holy Spirit working in their life.
In Jesus' name, we pray. Amen."
May God guide both of you according to His will. Continue to seek Him, trust Him, and rest in His love for you.
Prayer Focus: God, Thank You for loving me. Thank You for loving me, Jesus. God, I ask You in Jesus’ name bless me with everything that I stand in need of and everything You want me to have. Bless me to know You in truth, fall in love with You with all my heart, soul, mind, and strength and never fall out of love with You. Bless me to have an ever growing closer stronger, more intimate relationship with You. Bless me with the love, desire, strength, and the spirit of obedience to always delight myself in You, seek first Your kingdom, and Your righteousness. Help and strengthen me God to always respect and obey You. Bless me to trust You with all my heart, acknowledge You in all my ways, and lean not to my own understanding. 
