Is it recommended for the husband to recite a supplication at the time of the marriage contract?

If what is meant is the supplication at the time of the marriage contract, then it is sunnah (definition) to recite Khutbat al-Hajah (definition) (the Sermon of Need).

However, if what is meant is the supplication upon entering upon the wife, then it is sunnah for the man to take hold of his wife's forelock and say: "O Allah, I ask You for the good of her and the good of what You have instilled in her, and I seek refuge in You from her evil and the evil of what You have instilled in her," and then they pray two rak'ahs together as a congregation.