Hindi children rhymes is called Bal Kavita. These are poems written for children in Hindi.
Example of a bal kavita is the following poem by Suryakumar Pandey- Ek paan ka patta, ja pahuncha kalkatta, pakde apna mathha, Mila wahan par kathha. Aage mili supari, sabne ki taiyarri, pahunche fir sab poona, laga wahaan par choona.
References
Bal kavita Wikipedia(Text) CC BY-SA