PA-28-180 pilot reported during takeoff; the engine started sputtering. They didn't have any runway remaining to abort so they decided to climb out and did a 180 degree turn back to land.

Narrative

We flew in VFR conditions from ZZZ1 to ZZZ. After a full stop taxi back at ZZZ; we took off on runway XX. Winds were variable at 6. Upon takeoff; the engine started sputtering; and although at full throttle; we could not climb. Since we did not have any runway remaining to abort the takeoff and land back on the runway; I decided to continue flying out; trying to climb. There were no obstacles or terrain on the departure end of the runway. I only gained about 300 feet AGL. I flew out for about a mile before making a 180 degree turn back to land on runway XY; keeping my bank small as to not over stress the aircraft at a low altitude and airspeed. We landed back on runway XY; taxied off and did another run up; where we found that the right magneto was dead. We parked the plane and shut down; and called the rental business owner. Per the owner and mechanic's advice; we troubleshooted by taking the p lead off of the right magneto and attempting to do another mag check; but after no success; we had maintenance fly to get the airplane and we flew a different plane back to our original departure airport.