score:3
China's visa rules are rather simple in this matter, if you are applying for a visa in a country other than your citizenship, then you need to show proof that you are residing / traveling legally in that country. If you can not prove that you are in the USA legally using your Irish passport, then you have no choice but to apply with your US passport.
While you could try the excuse that you are leaving on another trip and can't leave your US passport behind. But there is a good chance they will levy the USA fee, even though they are stamping the visa in your Irish passport.
Upvote:0
Depending on the visa you are getting, you are eligible (thanks Obama and Xi Jinping!) for a 10 year tourist visa for 140 dollars. However, the period of which you are allowed to be in the country maybe is only 6 months. Overall validity of that tourist visa should be 10 years though, of course if the Chinese consulate deems you to not be a spy, have averse intentions, clean background, etc.
Look it up, it really exists as of a few months ago. Not sure if the Irish passport, or even any other countries with such a bilateral relation allows the same privileges.