The Shela HaKadosh says that Erev Rosh Chodesh Sivan is a special day to daven for your children’s spiritual and material needs. Here is an English Translation of the prayer he composed for this. You can say the Hebrew version here.
You have been the Eternal, our G-d, before You created the world, and You are the Eternal, our G-d, since you created the world, and You are G-d forever. You created Your world so that Your Divinity should become revealed thorugh Your holy Torah, as our Sages expounded on the first word therein, and for Israel, for they are Your people and Your inheritance whom You have chosen from among all nations. You have given them Your holy Torah and drawn them toward Your great Name. These two commandments are, “Be fruitful and Multiply” and “You shall teach them to your children.” Their purpose is that You did not create the world to be empty, but to be inhabited, and that it is for Your glory that You created, fashioned, and perfected it, so that we, our offspring, and all the descendants of your people Israel will know Your Name and study Your Torah.
Thus I entreat You, O Eternal, supreme King of kings. My eyes are fixed on You until You favor me, and hear my prayer, and provide me with sons and daughters who will also be fruitful and multiply, they and their descendents unto all generations, in order that they and we might all engage in the study of Your holy Torah, to learn and to teach, to observe and to do, and to fulfill with love all the words of Your Torah’s teaching. Enlighten our eyes in Your Torah and attach our heart to Your commandments to love and revere Your Name.
Our Father, compassionate Father, grant us all a long and blessed life. Who is like You, compassionate Father, Who in compassion remembers His creatures for life! Remember us for eternal life, as our Forefather Avraham prayed, “If only Yishmael would live before You,” which the Sages interpreted as “…live in reverence of You.”
For this I have come to appeal and plead before You, that my offspring and their descendants be proper, and that You find no imperfection or disrepute in me or them forever. May they be people of peace, truth, goodness and integrity in the eyes of G-d and man. Help them to become practiced in Torah, accomplished in Scriptures, Mishnah, Talmud, Kabbalah, mitzvos, kindness, and good attributes, and to serve you with an inner love and reverence, not merely outwardly. Provide every one of them with their needs with honor, and give them health, honor and strength, good bearing and appearance, grace and loving-kindness. May love and brotherhood reign among them. Provide them with suitable marriage partners of scholarly and righteous parentage who will also be blessed with all that I have asked for my own descendants, since they will share the same fate.
You, the Eternal, know everything that is concealed, and to You all my heart’s secrets are revealed. For all my intention concerning the above is for the sake of Your great and holy Name and Torah. Therefore, answer me, O Eternal, answer me in the merit of our holy Forefathers Avraham, Yitzchak, and Ya’akov. For the sake of the fathers save the children, so the branches will be like the roots. For the sake of Your servant, David, who is the fourth part of Your Chariot, who sings with Divine inspiration.
A song of ascents. Fortunate is everyone who fears the Eternal, who walks in His ways. When you eat of the toil of your hands, you are fortunate, and good will be yours. Your wife is like a fruitful vine in the inner chambers of your home; your children are like olive shoots around your table. Look! So is blessed the man who fears the Eternal. May the Eternal bless you from Zion, and may you see the good of Jerusalem all the days of your life. May you see your children’s children, peace upon Israel.
Please, O Eternal, Who listens to prayer: May the following verse be fulfilled in me: “‘As for Me,’ says the Eternal, “this My covenant shall remain their very being; My spirit, which rests upon you, and My words which I have put in your mouth, shall not depart from your mouth nor from the mouths of your children, nor from the mouths of your children’s children,” said the Eternal, “from now to all Eternity.” May the words of my mouth and the thoughts of my heart be pleasing before You, Eternal, my Rock and my Redeemer.