Are there any mantras/stotras that a parent can chant for the well being (health/wisdom/ long life etc) of their children?
Here are some vedic Mantras from Atharva Veda that pray's various deities for well being of their children. Parents can also use these mantras through them or after proper consultation with priests or acharyas as these are vedic Mantras.
Atharva Veda Kanda 2 - Sukta 13 - Mantra 4 - Dirghayu Sukta.
This Mantra is chanted at the time of ceremony of wearing first garments to new born baby by parents. Here the Mantra pray to various powers of gods so that child could live long life (upto 100 years) .
एह्यश्मानमा तिष्ठाश्मा भवतु ते तनु : |
कृण्वन्तु विश्वे देवा आयुष्टे शरद : शतम ||4||
O child come sit firmly on this rock ,so that your skin will become firm as rock. May the godly powers make your age of 100 years.
Atharva Veda Kanda 2 - Sukta 28 - Mantra 5 - Dirghayu Prapti Suktam.
Here In this Mantra Agni Deva , Mitra-Varuna ,Aditi and Vishwa- Devas are asked to bless a child with various good qualities.
इममग्न आयुषे वर्चसे नय प्रियं रेतो वरुण मित्रराजन |
मातेवास्मा आदिते शर्म यच्छ विश्वे देवा जरदष्टिर्यथासत् || 5||
O God Agni give this child a life of 100 years and make him lustrous
(Tejasvi). O Mitra -Varuna make this child fit to give birth to his children.O Aditi Devi bless this child with utmost joy like a mother. O Vishwa-Devas make (bless) this child with special qualities and abilities.
Atharva Veda Kanda 2 - Sukta 36 - Mantra 1 -Pativedan Sukta.
Here this sukta prays to lord agni so that the girl child could get a husband who is wealthy and who is full of good qualities and prosprous. Here we can see parents concern / Prayer for marrige of unmarried girl.
आ नो अग्ने सुमतिं संभलो गमेदिमां कुमारीं सह नो भगेन |
जुष्टा वरेषु समनेषु वल्गुरोषं पत्या सौभगमस्त्वस्यै || 1||
O Agni let our this intelligent unmarried girl get a husband who is full of good qualities ,who is wealthy and prosperous. Let this girl child gets a fortune to live life with her husband. i.e. let she get married.