Great question! I was curious myself, so I went digging through the archives of the New York Times and the Chicago Tribune. The first mention of a regular delivery service for pizza (as opposed to a one-off catered event like the apocryphal 1889 story about the King of Italy) is in 1960 for the Tribune and in 1952 for the Times.

The Times story, published in January, was a short guide to restaurants that deliver food to your door as "a brief respite ... for housewives for whom the holidays meant much extra work in the kitchen."

Under the heading "Italian specialties," the story states:

"Most pizzerias have cardboard boxes large enough to hold even the hugest pizza so it may be carried home. But the Sorrento Restaurant and Pizzeria, 216 Avenue A, delivers this and several other typically Italian dishes as far uptown as Stuyvesant Town on the East Side. Assorted antipasto is 60 cents, manicotti, 75 cents, chicken cacciatore with spaghetti, $1.25. Desserts are also of Italian flavor; spumoni (25 cents a serving) is one."

I don't think this is a definitive answer, but the way the story is written leads me to believe that home pizza delivery was a relatively unusual phenomenon even in 1952. Why else would the story refer only to this restaurant?

In 1956, a Times story explained that the first pizzeria in the United States was believed to be Lombardi's in New York City, which opened in 1905. The story went so far as to explain (tongue-in-cheek, I believe) what exactly a pizza is.