There's a new policy regarding Apple Care and Apple Care Plus. You can ONLY order it online when you order a product. Otherwise you have to do it via phone (1-800-275-2273).
When I ordered my iPhone 5 and later an iPad Mini, I was told by Verizon that I had 30 days to purchase Apple Care. Went on-line and could find no BUY button in any of the Apple links. Finally did it via phone and Apple rep told me "No more boxes via mail, just emails confirming the purchase(s).
If you are a registered Apple customer, you'll still need the Serial Number of the products.