Thanks, folks. This guy may offer a solution. Anybody want to do a sanity check on what he says?
He obviously is from a part of the world where mains power is 240 volt 50 Hz. For us in the USA most of his comments still apply as long as you understand that our mains power is 120 volt 60 Hz. Chargers in our part of the world are designed to run on nominal 120 volt 60 Hz power.
The Xantrex (one of the better brands of inverters and chargers) TrueCharge he mentions has now been replaced by the TrueCharge2 which has a number of advantages over the average charger. First, it has multi-stage or "smart" charging which lets the battery charge most of the way at a very high charge rate, and then automatically slows down as the battery reaches full charge. Second, because it is "power factor corrected" it is an easy load for a generator to drive. This is a particular issue for inverter generators, which can't deliver momentary surges of power a lot higher than their nominal maximum power output. Last, this charger is UL Listed, which means it has passed the UL safety testing and will not burn your house down or cause the batteries to explode.
UL Listing, by the way, says nothing about how well a given product works, only that it will not kill you or burn your house down. UL stands for Underwriter's Laboratory and was founded by insurance companies trying to determine what products were safe to let their customers use. As long as you understand that UL Listing is not a rating of "quality" you will do fine.
Here's a possible candidate for a battery charger:
I do not think that is a good candidate.
1) It has an "inrush current" of 40 amps. That means it would need a generator with a 4800 watt or higher surge rating to start the charger.
2) It has a maximum current draw of 21.8 amps. That means it should be used with a generator with a 2616 watt or higher continuous power rating. Your little generator is too small to drive this charger.
3) It is not UL Listed. To me that is a red flag that there is something about this charger that may not be totally safe.
A much better choice would be the 20 or maybe 40 amp versions of the TrueCharge2 charger. Your generator with a 900 watt power output should be able to easily power the 375 watts needed by the 20 amp TrueCharge2, and might even be able to power the 750 watts needed by the 40 amp TrueCharge2 depending on how good a job of controlling the inrush current the power factor correction circuitry does.