The 12 volt coil actually operates on about 9 volts through the resistor, so it would definitely be under powered with just 6 volts.
If your 12 volt charger has a trickle charge setting you could try it. Does it have an amp meter on it? The battery should charge safely at about 5 amps or less. I would pop the caps off, make sure it's full of distilled water, then turn the charger on for a second or two and watch that amp meter. If the charger is trying to put too much charge into it turn it off and look for a 6 volt charger.
