I've just finished my last infant ticket with Delta a few weeks ago (youngest turns 2 in July) and it has never been easy either for myself booking or agents processing. Paper tickets are a joke - I know of no other TATL airline that still does paper tickets - VS, KL, AF all do e-tickets at the time of booking. To compound matters Delta will not mail paper tickets to an international address so if you're based internationally (like me) you have to buy at the airport. This introduces a whole extra level of pain. In five years of infant ticketing I've never met a check-in agent that had anything positive to say about the process. Add 45-60 minutes to your schedule to wait at the ticket counter if you have a good agent.

My advice is to get the infant ticket number or PNR when you book. This will lock in the price and you shouldn't have any issues if the ticket isn't processed for a couple of weeks. It should be 10% of the lowest available fair in your cabin so there is some incentive to booking early.

Frankly, I'm not sure there are enough folks doing infant tickets to raise a big enough stink to get anything changed. It's a bad system and has been for some time.