What Sound Guy said. "Coleman" is now a product brand name for part of RVP (RV Products). The picture he linked is from just aft of where the product label is. That label will have the Model Number which can be de-coded to its cooling capacity and other features. His pic is also relevant to your generator question because it's a "before" shot involving his installation of a start assist device. The Capacitor for the Compressor is on the Left in that pic. The one for the Fan is the smaller one on the right. The arrows next to that photo show what the start assist device looks like, and what it looks like installed.
Wiring one of those assists is easy. It has two wires which connect to the two wires of the Compressor Capacitor where you'll find spare terminal lugs. And there's no polarity issue. So you can easily install one, just be sure the POWER is OFF and THEN that you SHORT across the capacitor terminals before you handle them.
To your question, I believe our Coleman model is "eight-something" and it's a 15,000-BTU unit. We have a Class C with on-board ONAN 4KW which starts it effortlessly every time. The A/C also has a factory hard start kit.
When I first read your post, my mind jumped to the little Coleman "Polar Cub" A/C's that are 8,000 or 9,000-BTU. Size of the unit is probably have a 13,500 like Sound Guy suggests or a 15,000 unit. You'll need to find out which. We had a 13,500 and now a 15,000. The power demand of the bigger one is actually significantly higher.
I haven't worked with portable generators, so what I'm about to say is based on what I've read here about Portables, A/C's, and Hard Start Kits:
A 3KW or (paired 2KW) inverter generator should start either size A/C
A single 2KW inverter generator might start a 13,500
The "Champion" brand portables, IF equipped with a 30-amp RV receptacle, would likely work for you also.
Again, conjecture based on what others have said.