Have a Red max BCZ2500S string trimmer, goes Bang-----Bang

Starts fine then in 3-4 min. running goes bang----bang ----bang , not 4 cycling  ,then if it rests for about 4min. starts up fine again then starts the bang bang and slowly shuts off.. So i tore it down to clean it up lots of 15 year gunk, cleaned up the magnet on Flywheel and feet on coil  .. Reset the coil, gap put together , with new s/p ,and same thing bang bang shuts down ..its still got good hella compression ---- Carb rebuild or new coil ??? thanks.

Hello; I would elaborate, and also say the sound is also like backfiring, loading up on fuel then periodic spark , and bang bang = after about 4-6 min. running , it has good static spark test ,  your coil suspect sounds like a good answer  , checked price on new coil its around $100.00 so I guess i will look on Ebay for used..   I've actually had it for about 20 years, I just found a carb for it in my old inventory ,so I guess I changed it some time back , I have about 30 engines here on the farm, plus my vintage go-Karts (2cycle), so its hard to keep track, other than that its been trouble free .. Thanks for your time. Gus.