I don't have a credit card either and I was able to use a prepaid debit card to purchase a plane ticket both online and at the airport.
Most if not all airports should also accept cash to pay for a plane ticket so you should also be able to buy the plane ticket using cash instead of a debit or credit card.
But if you want to buy a plane ticket online you should be able to use the prepaid debit card to purchase a plane ticket like I did.