Liberty Mutual will be the 1st insurer and Am Exp the secondary. Conrad's does take Am Exp. Am Exp also offers premium auto rental coverage for 45 days at $24.00.
For anyone wondering if Amex will really cover an accident - my husband was visiting Switzerland a couple of years ago and accidentally put the car he rented in reverse and smashed the rear end against a pole. The rental company charged him 5K + for the damages and Amex covered every penny.