Unfortunately most of major airline ticket providers do not offer this type of payment. Although there are some exception: Hotwire has a "Bill me later" program what allows delayed payment. Here's what you have to do: make a search on the main
airfares page, check Hotwire and hit Compare. On their page select your itinerary and start booking. When you arrive to the page where you are asked "How would you like to be billed?" select "Bill me later" option.
Other solution for you may be
the
"Fly Now, Pay Later" program by American Airlines. - (2008-03-30)