First off there's no absolute rule that says you can't put a AC unit on a subpanel nor that the service needs to be increased.

The load (both the new AC and the existing loads) on the entire service as well as the subpanel would need to be calculated to see what the legal course of actions are.

Frankly, running central air on 100A service is likely to be cutting it thin.

The general consensus with the pros is upgrade to a 200amp main:

https://answers.yahoo.com/question/index?qid=20090318124922AA9c3We

It seems like most of the time an upgrade like this would be done most efficiently by installing a new main panel and making the old one a sub-panel. There may be other considerations that prevent this, like space. You might also desire to replace the existing panel due to obsolescence or decay.

Actually, it's not usually all that difficult to pull the exiting main and just put a 200A one with sufficient spaces. You have the convenience of also being able to run the new service conductors so you can scoot the new panel a little higher on the wall in many cases to give you more slack on the connections.