It is typical to find a corollary that following theorems, but is it right to use the word corollary for a statement following a conjecture, where the statement is true only if the unproven conjecture is true?

I think it's generally bad form to have a corollary dependent on an earlier conjecture. I recommend one of the following: Theorem: Assuming Conjecture A, properties X, Y and Z are true. or Theorem: Conjecture A implies X, Y and Z. Most importantly, it should be crystal clear that the result is dependent on the conjecture. 


I would write "Proposition Z: If X holds, then Y is true." Even if the deduction of Y from X were trivial, I think labelling this a corollary would be confusing. (After all, what is the statement "X implies Y" a corollary of?) However, I wouldn't have a problem writing something like "as we saw above, Y would be a corollary of X" later on. (The subjunctive voice is important here!) 


I'm reminded of the following story that I posted on my personal web journal a couple years ago:



Making a new Theorem environment that let you have the bolded part say "Corollary to Conjecture X" seems to me a good compromise of concise and unlikely to confuse anyone. 


The correct term for such an item is CONJOLLARY. ;) 

