but might 36v from a pair of panels damage the actuator circuitry?
So here's the deal. Lead-acid batteries look electrically like a voltage source/sink with a small series resistance, with the voltage level a function of state of charge. 2V/cell (there are 6 cells in series in a 12V battery) is nominal, and if I remember right, their open circuit voltage is something like 1.9V empty, 2.1V full. That covers 90% of their behavior.
Considering that, the "1W@18V" spec of the solar panel isn't going to be able to "win" against the battery, and the solar panel's voltage will be pulled down to battery voltage, delivering probably 0.055A (=1W/18V) at whatever the battery voltage is.
When a battery gets completely full, however, its series resistance goes up dramatically, and the voltage goes up, until there's enough voltage to start electrolysis of the fluid and you get H2 and O2 generation at the terminals and loss of the electrolyte. A lead-acid battery, depending on the type + manufacturer, has a certain recombination rate of H2 + O2 => electrolyte that it can handle; if you electrolyze at a higher current than that, it leads to permanent electrolyte loss (+hence capacity loss)
So there is a safe current that can be delivered to a lead-acid battery continuously, where its own self discharge due to electrolysis balances the charging current. It depends on the manufacture + construction. I wouldn't feel worried about a C/10 or C/20 rate of charge (where C = the current needed to discharge a battery in 1 hour). Garage door batteries are probably > 1Ah capacity so you should be safe with 55mA charging current.
HOWEVER -- I would probably put a (zener diode and resistor in series) in parallel with each battery, the zener diode being about 14V and resistor being maybe 10 ohms or so, so that it keeps the battery terminals from getting charged too far.
Also: if you can, wire each solar panel to each battery (and keep the diodes), rather than the pair of panels in series wired to the batteries in series -- i.e. try to connect the center taps. By doing so, you'll charge each battery independently. Otherwise, what can ruin battery life is if the battery voltages diverge -- the one with the higher voltage will tend to get overcharged, while the other one will tend to get overdischarged and not completely charged.
You do need more than 12 volts to charge a 12 battery. Also how do you know that your solar panel is producing even 12 volts? Just because that is it's rating doesn't mean it always produces that value. Do you have enough sunlight? Have you measured the output of the panel? Can you provide more information on the charge controller? If you did provide 24 volts to the charge controller, how much voltage will it apply to the battery which is important because 24 volts is probably too much. Your panel is rated at 12 volts and 5 watts. Thus, assuming it is getting sufficient sunlight, its maximum current is 0.42 amperes. At that level, charging a 4.5 AH battery, would take a minimum of almost 11 hours.
Best Answer
As you have described it, your solar cell configuration will not be able to charge the battery. To fully charge a "6 volt" NiCd battery you need a charging voltage that is somewhat higher than that...something like 8.4 volts.
Charging a 700mAh battery at 240mA could be dangerous, it's hard to know for sure without having any specifications for the battery. To make sure the charging is safe you would want to limit the current to about 1/10 of the battery's capacity, or 70mA in this case. Of course, that means it would take at least 10 hours to charge the battery and probably more like 20 hours.
Charging at higher rates requires pretty careful monitoring of voltage, current, and/or battery temperature. This is turning into a very broad topic so I suggest you do some more research and come back with specific questions.