Q. Are there specific Tehillim that should be said for success in raising erlichen children? Thank you.
A. Mishna Berura (256: 2) writes that those who help and inspire others to start early and keep Shabbos properly will merit having children Gedoley Yisroel. Shaarei Tzion (ibid. 6) quotes a medresh relating that Elkana deserved Shmuel Hanavi as his son, because he motivated others to be oleh regel and follow him to Yerushalaim. Similar guidance is to be found in the introduction (Teshuvos) of the Chasam Sofer, that one who merits the many is rewarded with success in the chinuch of his children. It is said that the Brisker Rov Zt"l mentioned, that he does not know any definitive eitze (counsel) to be successful in the chinuch of children, but one thing he is aware; that the ones who merited the many, always had good children, as the posuk in Tehilim (112; 2) says: "His seed will be mighty in the land, a generation of upright ones, which shall be blessed" (Otzar Hayedios p. 153).
Some (Shimush Tehilim) recommend reciting chapters; 33, 96, 97, 126 and127 for success with children. Others suggest different chapters.
Horav Shlomo Miller's Shlit"a opinion is that although, Tehilim recitation is a powerful tool in beseeching the good will of Hashem, so is tefiloh bekavono. Hashem listens to the tefilos of those who pray from the heart, as He did with our Patriarchs when they prayed for their children.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a