2000 Hyundai Elantra overcharging alt?

Why don't you explain what "cooking the coil pack" means and how you are concluding this.

It means it doesn't work. We have replaced it twice and we have to replace it again. the car turns over but we have no fire to the coil pack.,

I seriously doubt the coils are the actual problem. It may fire up after replacing them simply because of a small increase in KV but I suspect you have too much resistance in other parts of the secondary circuit after the coil. Also check that you are getting full battery voltage coming into the coil.

We checked the voltage output and it was 13.7. The coils were checked and they wouldn't discharge. What else should we be testing?

Coils just don't fail that way. There has to be a different issue.You are going to have to check power supply and ground pulse when this happens.

Could it be the ECM? How do you check ground pulse? When it doesn't work, I get power to all 4 connections on the coil pack.

No, you don't. You're testing it while plugged in and reading through the coil. You would need a noid light to test for pulse when it fails.Don't use anything else or you could burn out the module.