A student pilot and instructor combined to lose control on the landing rollout; exiting the runway; striking a runway light and damaging both main gear tires.

Narrative

I was training a student pilot with approximately 50 hours. This was our first flight together. The flight proceeded normally: we flew to another airport; did two touch and gos and one go around with no significant issues or problems. We then returned to our home airport. During the landing; the aircraft's nose was not aligned with the runway; it was cocked left. I directed a right pedal input to align the nose with the center line. The student's right pedal input was too much; and the nose was now cocked off to the right. I came on the controls; as we were getting close to touchdown at this point. Simultaneously; the student had made a left pedal input to correct the over-correction; but again was too aggressive with the pedals. We touched down cocked approximately 20 degrees left of center line. At this point I tried to correct the aircraft's heading; but I thought I might tip the aircraft if I tried too hard. Additionally; the student was on the controls; with full brakes applied; so my steering options were limited. I committed to safely rolling into the grass. We rolled off into the grass; striking one of the runway lights. The right tire was flattened; and the left tire had a noticeable flat spot. The flight was terminated; and the club manager was notified.