When I suggest to my students that we will write poetry and that they will enjoy the activity, they look at me like I am crazy. They can't write poetry and they sure as heck won't enjoy the process!
But there are ways to write poetry that make it fun to do.
First off, you need some tools. Many people like rhyming poetry but then get frustrated with themselves when they can only come up with lame rhymes-moon, June, spoon sort of things. The best tool you can have to solve this problem is a rhyming dictionary. Fortunately, there are rhyming dictionaries online:
RhymeZone
Rhymer
WriteExpress
Now the other problem that people face with poetry is that they tend to get one line that sounds clunky. That's because it has too many or too few syllables, or some of the stress patterns are not working. Rather than worrying about the technicalities of all this (iambs, trochees, pentameter, tetrameter, etc.), just find a song you like and write your poem so it fits that song.
The easiest songs to use are twelve-bar blues-like Elvis's “You Ain't Nothin' But a Hound Dog” (well, it was Big Mama Thornton's but Elvis bought it for $75). You can find those lyrics at: here. The nice thing about blues is that all of us have felt them and they are a great poem to start with.
Another easy form is the ballad form. The Eagles' Hotel California is an example of a ballad-a poem or song that tells a story. It has an easy rhyme pattern like twelve-bar blues-every two lines rhyme. Also, if you like Emily Dickinson, you'll notice that a lot of her poems have a similar rhythm and rhyme pattern to Hotel California, although they don't tell stories (http://www.bartleby.com/113/).
Writing poetry that rhymes and sounds good is not too hard. You just have to have the right tools-and here they are! Enjoy!