Outboard motors are designed to provide years of trouble-free operation, and nothing spoils a weekend outing like one that will not run properly. Maintenance on these engines is relatively straightforward, and many of them sit for an entire off season without being started. When problems do arise with the ignition system it is rarely the coil, but they do sometimes fail.
The coil on your outboard is a sealed unit. The body should be completely intact and free of cracks. If an oil-filled coil is wet on its outside surface, it is cracked and leaking. It should be replaced.
If the coil is weak or damaged it will produce less spark energy than it is designed to. This will produce a weaker spark at the spark plug gap, making the engine harder to start. Spark plugs that are continuously fouling can indicate a weak spark.
If the coil is not producing enough voltage it can cause the engine to run erratically. If the problem seems to come and go, such as smooth acceleration and then rough acceleration, it could indicate that the coil is not able to maintain a steady voltage output.
No Spark at Spark Plug Gap
If the coil has failed completely, it will no longer produce any voltage. Without the increased voltage of the coil, the energy at the spark plug will be insufficient to jump the gap. This will result in the outboard failing to start.