Praise be to Allaah.
You should pray to Allaah to make his weaning easy. There is no specific duaa for this particular matter, but it is OK to recite general duaas.
Among the duaas for children narrated in the Quraan are:
What the wife of Imraan said when she gave birth to Maryam (interpretation of the meaning):
The words of the Prophet (peace and blessings of Allaah be upon him):
Wa innee ueedhuhaa bika wa dhurriyyatahaa min ash-Shaytaan ir-rajeem (I seek refuge with You (Allaah) for her and for her offspring from Shaytaan, the outcast). [Aal Imraan 3:36],
and what the believer said (interpretation of the meaning):
wa aslih li fi dhurriyyati (and make my offspring good) [al-Ahqaaf 46:15].
Ueedhuka bi kalimaat Illaahit-taammah min kulli shaytaanin wa haammah wa min kulli aynin laammah (I seek refuge for you in the perfect words of Allaah from every devil and every vermin, and from every bad eye)
Allaahumma innee asaluka al-afu wal-aafiyah fi ahli wa maali (O Allaah, I ask you for forgiveness and good health and protection with regard to my family and my wealth).
It is also OK to make duaa by yourself with regard to this matter, such as saying, O Allaah, provide him with blessed food, hasten good nourishment for him and make his weaning easy, and make him independent by Your grace and mercy, and so on.
You should also consult with doctors and seek their help you may find that they can give you some good advice. May Allaah help you to do all that is good.
Sheikh Muhammed Salih Al-Munajjid