Based on my experience with Toyota's distribution, your dealer may be correct - although you may still be in luck. Unfortunately, Toyota likes to save costs by distributing only a few different option combos on lower-margin vehicles. The Yaris is one of these low-margin vehicles. In other words, it's very hard (basically impossible) to pick-and-choose individual options.
I checked the Greater New York Regional website for Toyota.com, and the Yaris liftback is indeed only listed as an automatic, and with only two option combos. Based on this info, your dealer may be correct. On the other hand, the Midwest Regional website for Toyota.com (where I am) also only lists the automatic for the liftback... and I was able to get a manual liftback through my dealer.
The bottom line is that you probably can get a Yaris liftback with a manual tranny and airbags, but your dealer will have to turn over some rocks. This is the problem - since the dealer isn't making much profit, his motivation to do the legwork is low. You may find that, in order to get the airbags, you may have to buy other "packaged" options that you didn't want to get. Such is the joy of the Toyota low-cost distribution setup. Either hammer the dealer to get what you want or find another who will. The configuration you want is out there...
Sorry to write a boook on this, but I've met others that didn't know this. Just thought I'd share.