Repeat often. The more often a child hears a certain Bible passage the more likely he is to remember it. So, find as many opportunities as possible to recite the passage to the child. You can have him write it out, if he is old enough, which also helps with memory retention.
Help her understand what she is memorizing. If the child understands what the Bible passage is about, she is much more likely to memorize it. So sit down with her and explain what the Bible passage is about, and let her ask you any questions she may have.
Have fun. You can help children memorize Bible passages through game play. You can play a version of "trash can" basketball, where children get to split up in teams and play against each other to see who knows the most Bible passages. Word scrambles and crossword puzzles are also fun ways to help with memorization.
Make it a visual thing. Many children are able to retain information better though visual aids. Let your children draw pictures of what the Bible passages mean to them, to help them cement the memory.
Let them teach each other. Let a few children in the class take over teaching for a day, and have them teach the rest of the students the Bible passage.