Hi Peter,
I would attack this on three fronts.
1. Battery voltage available on cold start.
2. Possible rich mixture on cold start.
3. Failing coil.
1. With a volt meter measure the battery voltage at the battery before starting cold. Make sure connection is clean and tight. You should see 12.5 volts. If you see something less, your battery may not have enough voltage and subsequently you will have less voltage available at the coil.
2. A carburetor that is set too rich on a cold start will be difficult to start. This effect will disappear on a hot start as the fuel is easier to ignite as it gets atomized more easily.
3. You need to check the secondary resistance also. This is measured from the center plug cable tower to one of the side terminals. On a Bosch Blue coil this should be around 7800 ohms I believe. Primary resistance between the two outer terminals should be 3.4 ohms.
The 123 Ignition people state that their ignition system will work with any coil with a resistance of 1.0 ohms or higher. They recommend the Bosch "Blue" coil with a resistance rating of 3.4 ohms. I don't think I would use a coil with a rating less than 2.5 ohms. I also don't think you have to use a Bosch coil. I would target a coil with 2.5 - 3.5 ohms, and make sure the coil is rated as 12v, not 6v or 9v. Do not use a ballast resistor.
Interestingly enough, on the USA 123 Ignition site and the Dutch site they recommend the 126 style double wasted spark coil for use with the version of the 123 Ignition that eliminates the distributor cap and rotor on a 500 or 126 engine. I don't see them recommending a ballast resistor. This would be a resistance of around 1.5 ohms, which is within the spec that 123 recommend. Interesting. If your 123 is the type with the distributor cap, then I think you're supposed to use the recommended Bosch Blue coil or something with around 3.0 ohms.
http://123ignitionusa.com/123-fiat-for-fiat-500-and-fiat-126-special-order-non-stock-item/
http://123ignitionusa.com/123-4240-to-combine-with-123-fiat-double-coil/
http://www.123ignition.nl/products.phtml?brand=fiat 500
As you have pointed out before, there is surprisingly little information provided by the 123 Ignition people. I have the Pertronix system in my current 500 (works great) and the Pertronix folks offer more information which I think is valuable and applicable to any electronic ignition system as far as proper coil testing and use. I copied their information below. They recommend a 3.0 ohm coil.
What type of coil can I use with the Ignitor™? How do I check my coils resistance? (12V negative ground only)
To determine if your systems coil is compatible with the Ignitor, some measurements should be taken prior to installation of the Ignitor. Caution… While performing this test, never leave the ignition switch on for more than 30 seconds at a time.
Set your voltmeter to a 15 or 20-volt scale. Attach an 18 or 20 AWG jumper wire from the negative coil terminal to an engine ground. Attach positive (red) lead of your voltmeter to the positive side of the coil, and the negative (black) lead to an engine ground. Turn the ignition switch to the run position. Now read the voltage at the positive coil terminal. Turn the ignition switch off. If the voltage measured is approximately 12 volts, no resistance wire is present. A typical resistance wire will provide 9 - 6 volts.
The next step is to determine the resistance in the primary ignition. Label the wires attached to the coil terminals and note their appropriate location. Make sure that the ignition switch is off and disconnect all wires from the coil. Adjust your meter to the lowest ohm scale. If you are using an analog style meter make sure to zero the needle.
Measure from the negative terminal to the positive terminal. Write your measurement down.
Now the maximum system amperage can be determined, divide your voltage measurement by your coil resistance measurement. This will give you the system current or amperage.
Four and six cylinder engines should not exceed 4 amps. Eight cylinder engines should not exceed 8 amps. If the total amperage in your system is higher than the amount recommended for your application, you should install a ballast resistor.
Example
Voltage 12
Resistance 1.5
12 / 1.5 = 8
Total amperage 8
What will happen if I leave the ignition switch on when the engine is not running?
Leaving the ignition switch on when the engine is not running, can cause permanent damage to the ignition system, and related components. This does not apply to the accessory position of the ignition switch.
Can I change the length of the Ignitor™ wires?
Yes, the Ignitor wire length may be tailored to your specific needs. Occasionally the wires may need to be extended. We recommend that a 20-gauge copper strand wire be used. Make sure that all splices are cleaned, secure and insulated.
What should I gap the spark plugs to?
The Ignitor has no set specification in which the spark plugs should be gapped at. Every engine responds differently to spark plug setting. In most cases increasing the factory recommended gap by .005 improves the engine performance.
John