I also had a DOA charger from China, though not from PING. After some reserch I have done the following:-
Any lifepo4 with full BMS just needs a less than 5amp charger as the BMS shuts off each fully charged cell. You just need to work out the cell number and set the voltage accordingly
So for a 25.6 volt battery (24volt) would be 8 x 3.2 volt cells you can charge each cell at up to 0.7 volts over nominal max therfore set the charger voltage below 31.2 volts, the replacement charger I got (free of charge!!) outputs 28 volts which is a good middle ground at 3.5 volts a cell.
38.4 volt battery (36volt) is 12 x 3.2 and charge at 12x 3.5 = 42volts
You must ensure the current output is limited to 5 amps as this is the max for most cheep lifepo4 batteries due to thermal constraints.
The BMS will also shut down the battery if it detects a large drain on any cell - dont panic as you just need to plug in the charger again to reset -I have had this once when the battery was new and I had not realised the charger was not charging. After a few cycle charges the battery capacity has increase.
Below is a link to a little youtube vid, you can see the battery and charger mentioned. You might also notice no duct tape as this one seems better constructed than ping's and others - for a start it is fused and has a proper charging connector also heavy duty black plastic shrink and insulating sheets have been used and the BMS is part of the battery and not swinging around by its wires in a plastic tube!
YouTube - lifepo4 battery fitted to my cyclone electric bike