Is there any supplication, verse, chapter (Surah), or name among the Beautiful Names of Allah that can be recited solely to improve a two-year-old child's ability to breastfeed, given that he consumes neither milk nor food?

To facilitate the weaning of a child, supplication (du'a) is generally permissible, and there is no specific du'a designated for this. Among the supplications from the Quran are: ﴿وَإِنِّي أُعِيذُهَا بِكَ وَذُرِّيَّتَهَا مِنَ الشَّيْطَانِ الرَّجِيمِ﴾ (And I seek refuge for her in You and her offspring from Satan, the expelled) and ﴿وَأَصْلِحْ لِي فِي ذُرِّيَّتِي﴾ (And make righteous for me my offspring). From the Sunnah (definition) are: "I seek refuge for you in the perfect words of Allah from every devil and every harmful thing, and from every envious eye," and "O Allah, I ask You for pardon and well-being in my family and my wealth." There is no harm in supplicating with specific personal prayers such as: "O Allah, grant him blessed food and hasten good nourishment for him, and ease his weaning, and enrich him from Your grace and generosity," while also seeking assistance from doctors' advice.