If you have a constant current trickle charger, you can simply connect the 6V battery to the 12V charger and it will be fine. Do make sure to check the short circuit current of the charger so that it is below C/10 of the battery you are charging. You might not want to let the charging proceed to completion (i.e. do not top off).
For high current chargers and dead batteries, no, since it may cause reverse polarity in one of them. This is why you should not completely discharge multi cell batteries.
For high current chargers and batteries that are not completely dead, you can if you monitor voltage of each battery separately. You have to do this when they are not charging after a suitable rest time (which may be in minutes). Consider that, the end point of charging is determined not by how much current has passed, but by the final voltage of the battery. However, one battery will likely finish charging before the other one does. At that poin, it may be possible to top off the less charged one with low current.
IMHO, it may just be easier to charge each one separately, with a 7V output constant current buck converter charger for each battery, with both chargers operating from the same 12V supply.