That second syllable is not core
schwaCoriaceous carries its stress on the third syllable. The two in front of it are unstressed and their vowels are barely present.
heard ascoreaceous
spelledcoriaceous
saidko-ree-AY-shus
It is the -ri- of corium: coriaceous.
Said aloud the word does open with something very like the word core, and an ea is a normal English way to write that sound. But the i in that position is the whole of the link back to corium, leather, and losing it leaves the word with no visible root at all.
Also on this leaf
coriaseus corriaceous coriaseous coriaceus ceriaceous
All six are on the same page. All 6 spellings of coriaceous.