12 v dc led lights in parallel
Actually, I'm not sure that Tony's idea will help, because the surge that is tripping the over-current fold-back of the power supply is occurring when the string is first powered.  At that time, the PTC resistor will be cold, and have low resistance; by the time it heats up, the supply may have already shut down.

Actually, a simple small-valued resistor may be all that's necessary.  A resistor of 4 ohms (3.9 is the closest standard value) would limit the supply to its maximum rated current, but would also reduce the operating voltage of the LEDs to around 6 volts, which would no doubt result in unacceptable dimming and wasted power (about 10 watts).  However, you might try just using a 1 or 1.5 ohm resistor; this would limit the maximum current to 12 amps while the LED capacitors charged, but only for a few milliseconds; the power supply might just ride that out fine.

I had a similar problem with a switching adapter, but one where the LED string didn't even have the capacitor across the line.  In my case, the problem was that the (cheap) switcher couldn't start up under near-full load.  The solution in my case was to put the on-off switch on the 12-volt side rather than in the 120-volt line.  This of course results in the supply being powered up all the time, but once fully started, it had no problem handling the load of the LEDs being turned on.