Can I buy an Apple care plan for my iPad within a year of purchase. If yes, how do we do it online?

AppleCare coverage can be added up to 60-days after device purchase - after which, the opportunity is lost. Unless added at point-of-purchase, the device must be remotely tested or inspected prior to cover being accepted.

Buy an AppleCare plan – Apple Support

Link works for me, so its an issue your end.

It was a link to the apple care plan and how to buy online