I had a new coil installed on my 2004 Harley Davidson and it burned up after riding a few miles. I tried again and the same thing happen. What do I look for next.

Primary side or secondary side?
Did the same side burn both times?
You said you had the coil replaced. Where any tests were done on other ignition components?
I'm not a Harley mechanic but I'd say you'll need to look for whatever is causing the excessive draw through the failed circuit, primary or secondary.

Check for high resistance in the secondary (e.g. wires). It may be so high the path of least resistance is through the coil to ground. On cars, this typically happens because of old distributor caps, rotors, and spark plug wires.

Are you using the same spark plugs and Ignition Control Module that came in the bike?