You can engage children in a word association game by saying "cat" for instance and having them list all the words they associate with that animal. Then you can write up this list for them as a kind of poem. Maybe they can add to it by drawing a picture or making a collage of cats.
For older children found poetry can be a really fun way to pass a rainy afternoon. You can take old magazines and newspaper and you can cut out words or whole sentences to create poems. It's fun to use a particular article such as a story about the moon and have your child rearrange the text to make a new story or poem about the moon.
Another wonderful exercise, if you have a few children to entertain, is to do a kind of exquisite corpse poem, taken from an old parlor game. This will teach them how to collaborate on a project. Have one person write a sentence and fold the paper over just so that one sentence is revealed and pass to the next person. They then write a line in response and fold the paper so that only their line can be seen by the next person and not the original line. Keep sending it around and then read it aloud once it's gone around once or twice.
You can also have your poem take the shape of what it's about, If it's a rainy day and you are writing about rain, make the poem in the shape of a rain drop, or if it's a long poem each stanza in the form of a rain drop.