Is it permissible to swear in supplication by saying: "We adjure You to forgive us"?

There is no objection to a righteous and upright person swearing by Allah in matters of good, for Al-Bara' ibn Malik, may Allah be pleased with him, did so. On the authority of Anas, may Allah be pleased with him, that the Messenger of Allah, peace and blessings be upon him, said: "How many a weak, downtrodden person, owner of two worn garments, if he were to swear by Allah, Allah would fulfill his oath, among them Al-Bara' ibn Malik." And Al-Bara' swore by his Lord that He would grant them the shoulders of the polytheists, and He granted them to him.

As for matters of evil, it is not permissible to swear by Allah concerning them. Indeed, the deeds of a man were annulled because he swore that Allah would not forgive another, so Allah Almighty said: "Who is this who swears by Me that I will not forgive so-and-so? Indeed, I have forgiven so-and-so and invalidated your deed."