What is a Segulah to have children?
Rav Kaduri ZTz"L used to tell people to recite Tehillim 102 and 103 everyday just before Shkia and then say this little prayer: ירמיאו''א שיהא חשוב ומקובל ומרוצה פרקי תהלים שקראתי לפנך, ובזכות אותיותיהם ונקודותיהם וטעמיהם והשמות היוצאים מהם מראשי תבות, ומסופי תבות וחלופי תבות ובזכות אבותינו הקדושים אברהם יצחק ויעקב משה ואהרן יוסף הצדיק ודוד המלך עלהם השלום שתפתח מזלי ותתנני לחן וחסד בעיניך ובעיני כל רואי ואפקד השנה בזרע בר קימא בנים ובנות לעבודותו יתברך
There is also the 10 posukim of the Ramban.
Shiluach HaKan! The Midrash expounds the verse "v'es habanim tikach lach" (and take the children for yourself) in the passage that describes this mitzvah, as alluding to the person meriting to have his own offspring. For more details, see here in Sefer Shaleiach Tishalach and the next three pages.
[Note: In case anyone thinks of suggesting the "segulah" of being a kvatter at a bris, I challenge them to find a source for this. By all indications it is a very recent idea that has no basis.]
I believe the Derech of our Torah is that their are no magical actions that we do to yield some result. If we use the Torah as our guide, we see that Tephilah is the method our Avot and Imahot used to raise their level and relationship to Hashem so that they may merit providential assistance to having a child. The Torah did not tell us that Yaakov carried the baby at someones Brit, rather he prayed directly to Hashem.
HaRav Elimelech Biederman Shlita in his popular 'Torah Wellsprings' weekly parsha sheet writes in Parshas Vayeira 5781 the following:
The Baal HaTanya zt'l told the Magid of Mezritz zt'l, "It's already 24 years after my chasunah, and I still don't have children." The Magid told him to perform hachnasas orchim, and he will merit children. As it states (Tehillim 119:9), במה יזכה נער, "How does one merit children? את אורחו, by hosting guests."
The Magid added, "The father of the Baal Shem Tov also merited his child in the merit of hachnasas orchim. This is as it states הא לכם זרע (Bereishis 47:23), and ה״א is roshei teivos for הכנסת אורחים. This implies that with hachnasas orchim one can merit זרע, bearing children.
In this week's parashah, Avraham Avinu was ninety-nine, and Sarah Imeinu was eighty-nine, and they were both barren. In the merit of hachnasas orchim they bore a child the following year. The Ishah Shunamis also bore a child in the merit of hosting Elisha HaNavi. As it states (Melachim 2 ch.4), "One day, Elisha traveled to Shunam. An important woman lived there, and she convinced Elisha to eat bread by her. From then on, when Elisha was in Shunam, he ate there. The woman said to her husband, 'I know that he is a holy man, a man of G-d. Let's build a nice room for him upstairs, and we will place there a bed, table, chair, and lamp. When he comes to us, he can go there. [The next time Elisha was in Shunam] he went to this room… Elisha asked Geichazi (his servant), 'What should we do for her [in exchange for this favor]?' Geichazi replied, 'She doesn't have children…' Elisha said, 'Call her.' She came and stood in the doorway. Elisha said, 'You will bear a child…'"
She merited this child in the merit of hachnasas orchim. The Midrash (Tanchuma Ki Seitze 2) states, "There are mitzvos whose reward is children, like Sarah, who hosted guests, and the Shunamis [woman] who hosted Elisha." Women were cursed (Bereishis 3:16), בעצב תלדי בנים, that they will have the pain of childbirth. עצב is roshei teivos for עיניה צרה באורחין, which means that women's nature is to be stingy with guests. If she won't have עצב, which means, if she is generous with guests, she won't have the עצב of בעצב תלדי בנים, the pain of labor, either.
On the words, "ויטע אשל" - (Bereishis 21:33) the Rabbeinu b'Chaya comments that the only other place where ויטע is written is (Bereishis 2) ויטע גן בעדן מקדם. To hint that for the mitzvah of hachnasas orchim one will merit Gan Eden. The rewards for hachnasas orchim are given even in this world. As we say every day, אלו דברים שאדם אוכל פירותיהם בעולם הזה... הכנסת אורחים , "These are the things that one eats the fruits [of his good deeds] in this world… ,hachnasas orchim". Many blessings come from hachnasas orchim. Those who engage in it are fortunate – in this world and the next world.