Motor inrush current can be 5-10 times full load amps (FLA on the compressor nameplate)  A generator has to be sized to large enough to generate the inrush amperage to start your motor.  Generally, a generator sized at 5 times motor FLA will start the motor, but not always.  The best way is to take your motor specs to your generator guy and get him to specify a generator that will start it.

My AC uses about 14 amps running, but pulls 99 starting.

The generator at my house is sized at 4 times FLA and does fine on the AC, but the lights blink and the generator growls when the AC kicks in, which is normal.  It's a 12 KW with a 3 ton AC, but that 12 KW rating is on propane, it's only 10.5 KW on natural gas, which is more than enough to continue normal usage at our house when the lights go out.  Incidentally, my AC was recently replaced, and the new one creates a greater inrush, even though it draws less FLA.  The reason is the design of high efficiency motors, they draw more starting current, not less.

There are some residential AC manufacturers who have a soft start for their AC units.  A softstart limits inrush current.  It takes longer for the motor to get to speed, but it requires less peak current to get there.  With a softstart, some generators sized at 2 times FLA can start a motor.  Another option is a hard start capacitor, which will also help, but not as much as a soft start

Also, your Tranquility 27 is two stage.  If your unit will start on the lower stage you will have a little less load.

Check with just about any stand by generator manufacturer's web site, and I am sure you will find a sizing guide.

There's a good one here:  http://www.gillettegenerators.com/sizing/sizing02.html

No, I don't sell those.