It has been said that there are few texts in Patristic material that indicate Christians prayed for the salvation of unbelievers. I think the case is rather that the effort in finding them has not been made.
Here are two from Justin Martyr’s Dialogue with Trypho 96.3 and then right at the close where Justin prays for Trypho and his friends (Dialogue with Trypho 142.3).
Also noteworthy is what Justin says about the common perception regarding the type of prayers that God hears: “who does not know that prayer is the most pleasing to God which is uttered with lamentation and tears, with prostrate body or bended knees?” (Dialogue with Trypho 90.4). Of course, in the context, Justin is seeking to show that Moses’ prayers during the battle with the Amalekites were nonetheless heard even though he was seated. The whole passage needs read, for it is a fascinating piece of early Christian exegesis to show that it is prayer through the crucified Christ that wins the hearing of God.