Graded readers designed specifically for adults learning Japanese as a foreign language might be the best bet for students who are uncomfortable reading children's books. If that is the case, look at the レベル別日本語多読シリーズ level 0 and 1 books.
図鑑 can be very useful to beginning language students because of the predominance of pictures and the terms that accompany them. Zukan can be used in class presentations (show and tell) to talk about places and foods and objects that a student wants to describe.
Here are two examples of a series of zukan:
There are 19 volumes in the Field Best set that cover all types of Japanese plants and animals. These titles with their beautiful illustrations and vocabulary would go a long way to helping students to understand the vocabulary they run across in poems and novels.
Another set of books that is mostly pictures is 「和」の行事絵本, Wa no gyoji ehon, in 2 volumes. Spring/summer and Fall/winter. It is available in Japanese and English. The nice thing about the English edition is that it includes the Japanese term for the event and the description is in English. So, a teacher can introduce Doll's Day or Tanabata in class and students can learn more about it in English.
But, if students like children's books, there are plenty of picture books that would provide leisure reading. Often we recommend folk tales, but if you are not careful folk tales are full of dialects and spoken Japanese that lower level students can't understand. Here is one series that actually uses です／ます and works well for 1st and 2nd year students.
子どもとよむ 日本昔ばなし （くもん）There are 30 volumes in this series now.