Ecuadoran-Swiss mountain runner and guide Karl Egloff set the speed record on Cotopaxi in December 2012, 1h15m ascent and 1h37m round-trip. Egloff's background, and his Cotopaxi and other speed climbing records are discussed in detail in an extensive interview with Ian Corless on the "Talk Ultra" podcast. The interview begins about 28 min. into the podcast.
We consider Karl's run SUPPORTED because he ran part way with Nico Miranda.
Karl didn't record seconds. The 1h37m time came from guards at the refugio. Photos of his watch show a descent time of right about 23m00s. So it is likely that the total time was in the higher end of 1h37m.