I think that the first looping coaster was built before the first corkscrew coasters. Turn of the Century had bunny hills and two corkscrews. They later removed the bunny hills and replaced them with two verticle loops.
The first looping coaster was the Centrifuge Railway built in the 1850's. The first corkscrew coaster was Corkscrew built in 1975 at Knott's Berry Farm.