How can you diagnose which coil is bad when there is no check engine light on?

If a coil (in a coil-pack arrangement) is bad then the engine is probably misfiring on two cylinders.

You can purchase plastic pliers that are designed specifically for pulling sparkplug wires while the engine is running.

Start the engine, pull one plug wire from the coil pack using the plastic pliers. (don't use metal, you'll get a shock that will change your attitude) Go through the plug wires until you find one that DOESN'T make the engine run worse when you pull the wire. To verify that THAT is the bad coil, pull the OTHER wire and see if it doesn't affect the way the engine is running.