Is it permissible to perform Salat al-Hajah (Prayer of Need) to supplicate for preventing a wife's divorce from her husband, and is there a specific supplication for that?

There is no specific supplication to avoid divorce, but one can supplicate with the reported prayers for uniting people and fostering affection, the supplication for worry and grief, and the supplication of Dhul-Nun. Furthermore, each spouse's knowledge and fulfillment of the other's rights contribute to family stability. As for Salat al-Hajah (definition) (Prayer of Need), there is no objection to supplicating with it with the intention of marital stability, based on the view that it is valid or permissible to perform it for virtuous deeds.