In general, you can't because of the unknown function of the controller.
In the case of a solar cell, there is little damage except back current, which, changes are, the controller deals with.
Obviously when you connect two batteries you effectively double the load on the charger, but it doesn't matter do much because it can only supply what it can.
One problem in though is that it will not be able to charge up to the same voltage. This depends on the circumstances.
Second, Two batteries in parallel are generally not a good idea because one will try to charge the other. Of course, since these are rechargeable batteries this actually helps the case. At some point, if both batteries can be charged then their voltages will come to rest at some common value.
The down size is that this can be dangerous if one fails and the other tries to charge it up.
So, this is what to do:
- Charge both batteries, more make sure they have similar voltages.
- Measure the voltages of both batteries.
- Hook up one battery and the charger then measure the voltage. Do a spark test(touch wire charger wire quickly on and off of the batter and see how much it sparks).
- If all the voltages are similar hook up both batteries. First do a quick spark test just to make sure it the same as one and no excess power seems to drawn.
- Let charge somewhere safe for a little while... keep an eye on it. Check for excess power consumption(heat), etc...
If all this passes, and it should unless your controller or batteries are bad, then it should be rather safe.
Get two proper rated fuse and/or thermistors. (this would be probably about about 1-2x the current required by the lamp... slow blow) and wire them in.
Basically since the charger is just solar power and probably is very weak, changes of anything happening is pretty slim. There is probably not enough power there to do much of anything.
The batteries are the real issue, as they could explode(unlikely but possible) and catch something on fire. Note that you have more than 2x the same chance as with one battery.
The controller may not function with 2x load though as it might have some "intelligent" circuitry. The only way to know is to test or investigate more. You could add some slight resistance to the batteries to get the load back to what the controller would want. Your only wasting solar power anyways.
I doubt there is anything that could go wrong. If you do some quick light tests then chances are you'll be ok. Of course the controllers could be designed extremely poorly but even in that case I can't see how they would have a problem.
TLDR;
The easiest thing to do is simply do some voltage measurements. Obviously the controller is meant to deal with "dead" batteries(within reason). If all the voltages look good then things should be good. It will take 2x as long to charge and there might not be enough daylight to make it effective but it should still "work".
