Are there exercises you can do to slowly correct a funnel chest?

Perhaps: Depending on the depth of the funnel chest upper body exercises can help mask the visibility of the defect. For example larger pectoral muscles from push ups will help mask not correct the defect.

Not usually: Funnel chest or pectus excavatum is a defect of the chest wall and the ribs and stenrum that form the chest wall. These structures can be very rigid in an adult and somewhat compliant in an adolescent. Exercise will help flexibility and develop muscle mass but not change the defect. The defect can be treated by a nuss procedure.