If you teach public or private school or if you home school, Seedlings/Continental Press has a really nice Resource Guide to go with some of their readers. Lots of activities to go with these books nicely designed for kids who are just learning to read - activities you can do through the day in other subject areas to reinforce and supplement what they've read in the reader. Check it out!
If you don't teach or home school you might still come away with some interesting ideas to go with Bible story lessons.
This is a list of book publishers (some Christian) that publish leveled readers. Here is the list of specific books. If you have reluctant readers you can put a lot less emphasis on reading (at every level), especially out loud, to save embarassing who are already self-conscious about it. (unless the other kids in your class are unusually supportive - not patronizing- making your class a good place to overcome that fear) You might also consider having among your take home resources some easy-to-read Bible storybook readers offering reluctant readers some different materials to practice with than the stories they read in school.
Maybe parents (and non-parents) would be willing to give books or give to buy books to go into a Sunday School lending library? Note: it's very hard for non-teachers (and non-parents) to choose appropriate books for the newest readers unless they know what they're looking for.
But these publishers and reading lists are a good place to start.