To my understanding, The Shelah prayer recited on Erev Rosh Chodesh Sivan is to ask for the success of the children, that they should go in the way of the Torah. Can it be recited by a single person (who is of of course without children)?

Greetings, The Shelah's prayer is not just about existing children, but the education of the children of a person in the present and future. Therefore it is permissible and proper also for a single person to pray for his offspring to grow up to be G-d-fearing. Besorot Tovot. This question was answered by Rabbi Avigdor Nebenzahl Yeshivat HaKotel