In my opinion, most new songwriters use too many rhymes. Rhymes are pleasing to the ear... but a lot of them have become cliché. Allow yourself a few obvious rhyming pairs (night/right, day/way, etc.) per song, but don't use them every line. There are other ways to make words sound good together. How about some alliteration (using words that start with the same sound, like change/challenge)? Or try assonance, which means using the same vowel sound with a different final consonant (make/hate). I use assonance a lot, to defy expectations about what the next line will be. Another fun kind of rhyme is the internal rhyme. These are harder to write, but if you can do it once in a while, it brings your lyrics to the next level. An example would be "I had a place to go/My face would show." Go/show is the main rhyming pair, but place/face also rhymes. Just be sure not to put rhymes everywhere!
Elizabeth Bruce - songwriting, voice & piano instructor