How to perform conducted emissions testing for electric generator?
Would using a constant load/current probe be sufficient for testing
  all frequencies?
  
  Is there a need for a LISN when testing a generator for conducted
  emissions?


Probably not, but only if your load is constant and doesn't create noise. Since an LISN is a filter used to block mains noise from your measurement, a current probe would probably suffice. But I'd imagine they'll use an LISN at the ETL, replicating their test setup would be best.


  Are there any online sources for procedural EMC testing of generators/power supplies? (I have googled many iterations to no
  avail.)


As far as I can tell, there aren't any direct requirements for generators as far as IEC requirements go. There will be saftey requirements. On most generators that I have seen an ETL sticker cannot be found on the outside or in the operators manual. Work with your product testing lab to see what you need or find a consultant.