The best way, if you have a multimeter is to hook up the lights with the normal batteries and use the meter to measure the current (Amps) that it is drawing. Set the meter for the AMPS scale, then put the meter in the path with the batteries (black lead on the positive end of the battery and red lead touching the wire that would hook to the positive end of the batery. Start with the highest amperage setting on the meter and work your way down until you get a good reading. A single LED is usually satisfied with 10 to 20 milliamps at about 1.5 to 3 volts, I expect your string is a mix of series and parallel strings that will likely draw in the 50 to 100 milliamp range, but I don't know. At any rate, once you know the current, just divide the voltage drop you want by the current and that will be the size resistor you need. Lets let the batterys are run down a little and they are at 4 volts.
If we use 100 ma:
12v - 4.0 = 8 volts that you want to get rid of. Just guessing 8v/100ma = 80 ohms. for the power rating, multiply the voltage and current - 8x100mili = .8 watts.
If we use 50 ma, the resistor becomes 160 ohm and .4 watts. A better option would be to hook three strings in series ...