How to buy AppleCare+ for my new Apple Watch?

If you are in the U.S., see the following from AppleCare Products - Watch - Apple

How to buy

1. Purchase AppleCare+ with your new Apple Watch.
2. Or buy it within 60 days of your Apple Watch purchase:

• • On your paired iPhone (go to the Watch app > General > About and choose AppleCare+ Coverage Available)
  • Online (requires you to verify your serial number and run a remote diagnostic)
  • At an Apple Store (inspection of Apple Watch and proof of purchase are required)
  • By calling 800-275-2273 (requires you to run a remote diagnostic and provide proof of purchase)

If there is no option in Settings on your iPhone as described: On your paired iPhone (go to the Watch app > General > About and choose AppleCare+ Coverage Available)

then try one of the 3 other options shown in my previous reply.

Did you use the last option (or at least call that number to see if you can find what the problem is)?

By calling 800-275-2273 (requires you to run a remote diagnostic and provide proof of purchase)