What is the ruling on supplicating that God not forgive someone who has wronged me?

It is permissible for the wronged to supplicate against their oppressor, as Allah Almighty says: "Allah does not like the public utterance of evil, except by one who has been wronged" [An-Nisa: 148].

As for supplicating that Allah not forgive the oppressor, it is permissible if the intention is to not forgive regarding the right of the wronged person, not regarding the right of Allah Almighty.