Let's bring your request to God together, seeking His will for your cousin. We remember how God blessed Hannah with a child in 1 Samuel 1:17 (WEB), "Then Eli answered, 'Go in peace, and may the God of Israel grant your petition that you have asked of him.'" God is the giver of life and children are a blessing from Him. Psalm 127:3-5 (WEB) says, "Behold, children are a heritage of Yahweh. The fruit of the womb is his reward. As arrows in the hand of a mighty man, so are the children of youth. Happy is the man who has his quiver full of them."
However, we must also remember that God's blessings come in many forms, and His will is perfect. It's important to pray for God's will to be done in your cousin's life, which may or may not include many children. Let's pray for your cousin to trust in God's plan for their life and to be content in all circumstances, as it says in Philippians 4:11-13 (WEB), "Not that I speak because of lack, for I have learned in whatever state I am, to be content in it. I know how to be humbled, and I know also how to abound. In everything and in all things I have learned the secret both to be filled and to be hungry, both to abound and to be in need. I can do all things through Christ who strengthens me."
Let's also pray for your cousin's spiritual growth and that they may know Jesus Christ. It is much more important than just having children. The Lord Jesus Christ in Matthew 11:28-30 (WEB) says, "Come to me, all you who labor and are heavily burdened, and I will give you rest. Take my yoke upon you, and learn from me, for I am gentle and lowly in heart; and you will find rest for your souls. For my yoke is easy, and my burden is light."
Heavenly Father, we come before You in Jesus' name, lifting up the cousin of Anonymous. We pray that You would bless them with children if it is Your will, but more importantly, we pray that they would know Jesus Christ as their Lord and Savior. We pray for their spiritual growth and that they would trust in Your plan for their life. We ask that You would give them contentment in all circumstances and that they would find their rest in You. We also pray that Anonymous will learn to pray in Jesus Name for their requests and know that it is only by the name of Jesus that we have access to God. We pray that Anonymous and their family members will come to know Jesus Christ and believe in Him. In Jesus Name we pray. Amen.