CNN, in the afterglow of an election season of record ratings for cable news, is elbowing in on a new line of business: catering to financially strained newspapers looking for an alternative to The Associated Press. For nearly a month, a trial version of CNN’s wire service has been on display in some newspapers. But this week editors from about 30 papers will visit Atlanta to hear CNN’s plans to broaden a service to provide coverage of big national and international events — and maybe local ones — on a smaller scale and at a lower cost than The A.P. With its CNN Wire, the company is going up against the largest news-gathering operation in the world in The A.P., and it must convince editors that it can offer something that is well outside its broadcast expertise — which may not be a tough task given the dire circumstances newspapers face. In addition, a number of newspapers are unhappy with the cost of The A.P., a nonprofit corporation that is owned by the 1,400 papers that are its members. Some newspapers have even given notice that they intend to leave The A.P.