Tower Controller reported a departing light single engine aircraft encountered engine problems and returned to the airport and landed safely.

Narrative

I was training on local control and Aircraft X was cleared for takeoff Runway 13. While over the runway; the pilot reported a vibration and requested to 'maintain VFR' and land. Ceilings were low around 500 ft. but I immediately suspected a possible emergency situation and approved the pilot to make right or left traffic. Pilot then came back and advised they'd be unable to maintain VFR and requested vectors for an approach. I assigned them a heading of 360 and 3000 ft; issued them a clearance back to the airport; and called the radar controller to coordinate. After coordination; I switched Aircraft X to departure. Simultaneously; the other tower positions handled notifications and coordination for the emergency response. Another training team relieved us to work the remainder of the flight and the aircraft made an instrument approach and landed safely. This event was a good reminder that we should always be thinking about 'what if' scenarios so we're ready for it. It's also a good reminder for me to regularly review procedures in our SOP; LOAs; and the national orders.