This method was discovered in iOS 12.1.4.

1) Write down your credit cards in the order you want them: 1 through 10. 1 being your primary credit card. 10 being your least used.

2) Starting from the bottom, set your 10th credit card as your Default Card. (Watch app > Wallet & Apple Pay > Default Card) and tap the Back button.

3) On your Watch, double-press the side button to invoke Wallet to confirm your new default. Then press the Digital Crown to dismiss the Wallet. (I couldn’t get this procedure to work consistently without this step.)

4) Work your way up the list setting each card to your Default Card along the way (don’t forget step 3). When you are done your credit cards will be in your preferred order in the Apple Watch Wallet.