Joe Zeff, who ran Time Magazine‘s graphics department for a few years while I was there, is getting some attention for an idea he floated on his new Design Blog: publishers, he suggests, should lure readers to their struggling magazines by giving away free Apple (AAPL) iPads in return for paid subscriptions.

It’s a variation on the old Sports Illustrated sneaker-phone gimmick (see video below the fold), which worked 20 years ago because the phones were pretty cheap and the subscribers they attracted tended to become loyal readers.

But loyal readers are a dying breed in these of days of Google (GOOG) News and information overload, and publishers are desperately seeking new ideas that can resurrect their aging business models — including re-casting their print publications as iPad apps. (See the Sports Illustrated demo, also below the fold.)

A free iPad would certainly attract subscribers, but can magazines really afford to give away a tablet computer the way SI gave away sneaker phones? We ran the numbers, and the news is not good.

The best model for Zeff’s idea is the subsidized smartphone. AT&T (T) is happy to knock a few hundred dollars off the sticker price of an iPhone — or maybe even give it away — because they know that in return they’re going to get 24 monthly payments of at least $69.99, or nearly $1,680.

But magazines are not high ticket items. If Sports Illustrated were to trade a $499 iPad for a two-year subscription, as Zeff suggests, they’d be shelling out the equivalent of about $20.80 a month.

With discounts and special renewal offers, however, the average subscription price for a magazine like Sports Illustrated is about $60 per year (repeat: PER YEAR). At that rate, it would take Time Inc. (TWX) nearly eight and a half years per subscriber to work off its debt to Apple, by which time today’s iPad will probably look as primitive as 1991’s sneaker phone.

Meanwhile, Amazon (AMZN) is moving quickly to get as many of their tablet computers in readers’ hands before the iPad ships, offering selected customers free Kindle’s — at least free for one month — with a money-back guarantee “if you don’t love it” (and you can keep the Kindle).

Below: The old Sports Illustrated sneaker phone promo and the new tablet-ready edition.

[Follow Philip Elmer-DeWitt on Twitter @philiped]