I'm not sure if Coleman makes anything. "They" certainly do no make generators.
Correct. Coleman sold Powermate generators under their name. Not sure if Powermate went under or what, but Pramac brought Powermate back. Now Pramac power is in liquidation so who knows what the future will bring for non-generic parts. One thing to look out for, some Coleman gensets had an alternator endbell bearing pressed into a plastic housing. If you have one of those, make sure that bearing is always in tip-top shape - you don't want it overheating.
Who the hell let all the morning people run things?