I will look on mine tonight for 12 volt plug. I don't recall one near the kitchen. One is next to the table on the side of the TV cabinet. And of course 1 on the dash. An inverter to run a 120 volt coffee maker would require at least 900 to 1200 running watts. That's a medium size inverter unit and would require almost 100 amp at 12 volts to power the unit. It is doable but pricey, unless your husband wants a little project.
I do not own a 12 volt coffee maker but you may want to do a cost comparison.
What my wife and I do is run the generator for a short time to make cookies or nachos in the convection oven then turn the generator off. We find it only takes about 5 minutes for coffee or 15 minutes for cookies.
Hope this helps.