Of course, you can daven for someone to do teshuvah; one famous example of such a prayer that was successful is mentioned in the Gemara (Brachos 10a.)
It is become common nowadays to learn Torah, recite Tehillim, give tzedakah, or do another mitzvah on another’s behalf. (This has a logic behind it, but it seems to be a recent invention without ancient sources, and some question whether it works.) So you could dedicate a certain amount of Tehillim or learning to a person, with the prayer that the merits of your actions prompt Hashem to accept your prayer that the person repent.