Similar pronunciation but different spelling:
* Corps: This word is pronounced the same as "core" but refers to a group of people, especially a military unit.
* Coar (archaic): This word, meaning "to stir or agitate," has a very similar pronunciation to "core" but is rarely used today.
Same spelling but different pronunciation:
* Core: This word can be pronounced "core" (like the center of something) or "co-er" (meaning to force or compel).
Ultimately, the best "homonym" for "core" depends on the specific context you're looking for.