I don't have any students so no requests for specific classes played, but just for the record these are the subjects that cursebreakers are required to have NEWTs in: Arithmancy, Ancient Runes, Charms, Transfiguration, Defence Against the Dark Arts, and Potions. So although we don't have canon sources for what cursebreakers do, it stands to reason that those are the ones used most in the day-to-day of a cursebreaker's job and therefore the subjects a former cursebreaker might be most qualified to teach

Arithmancy and Ancient Runes are the two of those that are currently open (the others already have professors).

(But I think the golem idea is really cool also!)