Make sure what ever you ask for to make up for the inconvenience costs more than the AC and makes significantly more trouble for them than managing the installation of it. Checking your legal standing with a lawyer at this point is probably wise.
And start shopping for a new place ASAP. If you can’t live w/o AC, then you have to make sure you have a place to go.
My counter offer would be “I can’t live without air conditioning” and “you have x days to fix it or I’m moving out at your expense.”
