Helping out with coverage on sports when both teams are playing in town at the same time is a good way to break in with a paper. Maybe you won't get a lot of work at first, but all it takes is one or two assignments to show the editor or publisher the quality of your photographs, and you'll be on your way. Shoot some assignments on speculation, and then take them to the editor and ask if the paper can use them. If you should ever happen on the scene of a wreck or fire, these are potential sure sellers. Photograph these activities.
Weekly newspapers love to publicize such events.
Weekly newspapers love church related activities. Now, granted, none of these are earthshaking news events, but they're the kind of photos you see in weekly newspapers all the time. The reason you see them is that someone spent the time to shoot the photographs, and that weekly newspapers love to run photos of local people. Photographs shot on speculation are a good way to get started with your weekly newspaper. For the editor of a weekly newspaper, finding a parttime photographer who's dependable and who can take a decent photograph is like the answer to a prayer.