Coach battery on ours as well. I've found that it really needs to be up to snuff or the little ONAN 4KY won't crank.
What I want to add is this: Do NOT trifle with weak batteries! If "IT" (Generator off Coach Battery -OR- Road Engine off Chassis Battery) won't crank, either Jump it or Charge it or Go get a battery. Why? Genset has a fragile little starter that's as expensive as a road engine starter and twice as hard to change. Burn it up with cranking attempts on a low battery and you're in for grief. Road Engine? I had a call from a neighbor. His co-owner in the RV tried to start it with low battery. They took care of the battery and it still wouldn't start. Had to replace Starter and a Solenoid (Ford V10) to get it back running.
If it looks like you need a battery, get one. You'll be doing it anyway and at least this way you may not be fixing more besides.
