Book online, then call EK they should be able to do it.
If done through a travel agent, the travel agent is the only authority that can do it for you (since they will need to re-issue the tickets).

I once booked a reward SYD-DXB-BEY return in J, and called EK to ask if I was able to get the airpass booked; they said they could do it over the phone (this was in Aus of course, not sure about other countries).

I'm afraid you won't be able to do it over the counter at the airport; I've asked the very same thing before and they confirmed that the Airpass has to show as booked in conjunction with XX ticket.

Hope this helps.