Dampers aren't like open windows or doors in that a damper creates a significant pressure drop that's dependent on the velocity thru the damper. Damper sizing has to take into account both the cfm of the cooler and the static pressure it can develop.
Ideally you would want a fan curve for the cooler you have, and a velocity vs pressure drop curve for the damper you intend to use.
There's a generic damper curve at
http://www.engineersedge.com/hvac-systems/damper-pressure-drop.htm that's probably pretty close since the construction of most dampers is relatively similar. You currently have 2.33 sq ft of damper area, assuming the gable vent is rectangular and treating the vent as if its pressure drop is the same as that of a damper.
Assuming your cooler can develop 1/2" of static pressure, you can use the above linked curve to determine what your current outlet will handle. The curve crosses the 0.5" sp line at a velocity of 1500 fpm. 1500 fpm thru 2.33 sq ft would equal 3500 cfm. To move this 3500 cfm thru the openings, the entire building has to be pressurized to 1/2" sp. and if you assume the building is otherwise well sealed, then at that point your cooler is only handling 3500 cfm rather than its rated 6500 cfm.
The above is just air moving basics. I don't have specific knowledge related to swamp coolers because, in this part of the country, they're seldom used anywhere other than in commercial kitchens where the exhaust hoods take care of venting. So, I can't really say what sort of damper sizing criteria should be used to vent a cooler.
That said, my gut feeling is that there should be adequate damper area to vent the rated cfm at some pressure substantially less than the max pressure rating of the cooler. As you reduce the cfm the unit is handling, you will move closer to fully saturated air (100% relative humidity) in the building which will result in your insulation and everything else in the building that's capable of absorbing moisture becoming saturated. This also reduces the capacity of the unit and leaves you with much less actual cooling than the unit is capable of delivering.
The cooler manufacturer should be able to give you a recommendation for damper sizing. The info you have provided doesn't give enough specifics for anything more than a wild guess, and that's not good enough when you're pumping moisture laden air into a building for the purpose of cooling. Adding another 4 sq ft of damper would give you the ability to handle the full output of the cooler with a 0.3" sp drop thru the damper. That might be good enough, or it might not. This is the sort of thing that the cooler mfgr can tell you pretty much instantly.
